geometry Support percent algebra function domain Reaper

I think I feel for all evil tyrants. I understand how they feel. Does anyone else have this happen when they play nationstates? Is it the power that makes you go crazy? Is it the
not feeling like you are a part of a country?

Well this all started during world history-we were talking about-actually I forget who since this was a week or so ago and I don't have my notebook out-but the point is we were thinking about how dictators think.
 The question was asked. And easily answered by us nationstates(or Age of<anything>) playing students. Our answer was: We know from experience!

Do you think that these games are realistic enough to show that you'd be a bad leader or is it that since they aren't real people you can't tell.

By the way-I'm Prime Obsession,Breaststroke and co-owner of funcia in the region funcia(how different-i'm not myself)

well, i don't know the answer to your question. but u have to see the other side of the words in laws which are brought by u.

[url=http://www.nationstates.net/theta_shaowei]my nationstate[/url]  :maybe:

I have never even heard of nationstates :rotfl:

I'm gonna check it out right now :D

Yeah well I feel heartless and cruel and do things I would judge wrong if I were the people that didn't rule.

UN Category: Corrupt Dictatorship
Civil Rights: Good
Economy: Fair
Political Freedoms: Rare

The Corrupt Dictatorship of AoPS is a tiny, environmentally stunning nation, remarkable for its burgeoning human population. Its hard-nosed, cynical population of 5 million are ruled with an iron fist by the dictatorship government, which ensures that no-one outside the party gets too rich. In their personal lives, however, citizens are relatively unoppressed; it remains to be seen whether this is because the government genuinely cares about its people, or if it hasn't gotten around to stamping out civil rights yet.

The enormous, corrupt government devotes most of its attentions to Law & Order, with areas such as Social Welfare and Religion & Spirituality receiving almost no funds by comparison. The average income tax rate is 33%, but much higher for the wealthy. A substantial private sector is led by the Information Technology, Automobile Manufacturing, and Cheese Exports industries.

Crime is moderate.

SHOULD DEMOCRACY BE COMPULSORY?

"Compulsory voting makes about as much as sense as having the death penalty for attempted suicide," says civil rights activist Hack Hanover. "You can't force people to be free! You can only give them the choice. Besides, if all those derelicts who can't be bothered to get off their ass once every few years voted, who would they elect? I shudder to think."

UN Category: Corrupt Dictatorship
Civil Rights: Below Average
Ecnomy: Basket Case
Political Freedons: Outlawed

The Armed Republic of Asian communists of KS is a tiny, safe nation, remarkable for its complete lack of prisons. Its compassionate, cynical population of 6 million are ruled with an iron fist by the dictatorship government, which ensures that no-one outside the party gets too rich. In their personal lives, however, citizens are relatively unoppressed; it remains to be seen whether this is because the government genuinely cares about its people, or if it hasn't gotten around to stamping out civil rights yet.

It is difficult to tell where the omnipresent, corrupt, socially-minded government stops and the rest of society begins, but it devotes most of its attentions to Social Welfare, with areas such as Religion & Spirituality and Law & Order receiving almost no funds by comparison. The average income tax rate is 69%, and even higher for the wealthy. Private enterprise is illegal, but for those in the know there is a slick and highly efficient black market in Trout Farming.

Elections have been outlawed. Crime -- especially youth-related -- is totally unknown. Asian communists of KS's national animal is the fetus, which frolics freely in the nation's many lush forests, and its currency is the stem cell.

Asian communists of KS is ranked 369th in the region and 8,647th in the world for Most Extreme Nations.

UN Category: Democratic Socialists
Civil Rights:Excellent
Economy:Developing
Political Freedoms:Excellent

The Commonwealth of Mustafa15 is a tiny, socially progressive nation, notable for its burgeoning bullfrog population. Its hard-nosed, intelligent population of 6 million are fiercely patriotic and enjoy great social equality; they tend to view other, more capitalist countries as somewhat immoral and corrupt.

The large government juggles the competing demands of Law & Order, Education, and Social Welfare. The average income tax rate is 31%, but much higher for the wealthy. A tiny private sector is dominated by the Book Publishing industry.

Voting is voluntary and tourists from around the world come to visit the country's famous rainforests. Crime is moderate. Mustafa15's national animal is the bullfrog, which frolics freely in the nation's many lush forests, and its currency is the dojo.

Mustafa15 is ranked 2002nd in the region and 37,136th in the world for Most Extreme Nations.

CHILD CASINO SHOCK

Social activist Chastity McGuffin is outraged. "Gambling needs to be outlawed immediately. It's no wonder children are becoming sucked into the vice, with adults setting such a poor example. Gambling is a stain on Dymanite_go_BOOM's international reputation and it must be stopped!"

Compulsory Organ Harvesting Proposed

"It's not as crazy as it sounds," says Dr. May Thiesen. "Every day, people die because we don't have the organs to save them. Well, that and widespread under-funding of the health system. But the point is, if the government allowed us to take organs from dead people, we could save hundreds of lives a year. And come on, it's not like dead people need them."

mmm.... Nothing like the fresh smell of harvested organs :rotfl:

Cloning Research Promises New Breakthrough

"It's really very exciting," says lab head Chastity Longbottom. "Until now, we've kept very quiet, to avoid being targeted by lunatic fringe groups who for some reason think it's wrong to clone human embryos. It's too early to promise anything, but we hope that one day we will have genetic cures for a whole range of debilitating illnesses. I certainly hope the government will support our work."

Too Much Yakking, Already, Say Delegation

"These days, anyone says whatever they want with no regard to what kind of dribble is coming out of their mouths!" says angry commuter Roxanne Summers. "It's gone too far. We should go back to the good old days, when if someone started talking garbage, we'd smack them one."

Democratic Socialists
Civil Rights: Average
Economy: Weak
Political Freedoms: Some

Read Machiavelli's [u]The Prince[/u]

"Better to be feared than loved"

according to him. very interesting, tho old, book

Police Consider "Big Brother" Anti-Crime System

"Hey, I've got news for you," says Police media liaison Stephanie King. "When you're out in public, PEOPLE CAN SEE YOU. These cameras will be extremely helpful in reducing the national crime rate. Frankly, I can't see what the fuss is about."

Nazi Sympathizers Plan Rally

"It's exactly because we're civilized that we must let the demonstration proceed," says free speech campaigner Beth Wong. "We may not like what they have to say, but in this society, people have the right to argue whatever political view they want, no matter how hateful, selfish, or stupid it is."

Auto Industry Struggles Against Foreign Imports

"Unless this government does something, Dymanite_go_BOOM won't have an auto industry for much longer," says auto industry union boss George W. Mombota, in a rare public appearance alongside management. "These foreign companies employ people for a few snicker bars a day. The only way to level the playing field is to raise tariffs. The government would make more money, too, so it's win-win."

Dymanite_go_BOOM Awash With Red-Rimmed Eyes

"My factory's productivity is down ten percent since marijuana was decriminalized," complains employer Billy-Bob Winters. "And the number of thefts from the candy machine is off the scale. This so-called 'pot' needs to be banned in all public places. Let the junkies do what they want at home, but not in my workplace."

Citizens Struggle Under "Unfair" Tax Burden

"I don't object to the amount of tax, I object to where it's being spent," says social reformer Larry Clinton. "I'd like to see everyone have a choice as to where their snicker bars go every time they fill out a tax return. Everyone would feel a lot better about opening their wallets if they had a say as to where the money went. I think you'd see a lot more public money going to education and a lot less to business."

Budget Time: Accountants Excited

"The state of the education system is, in many areas, simply frightful," says Teachers Union leader Melbourne Hendrikson. "And even where we are doing well, we could do better. I appeal to the authorities for a substantial boost in funding. Remember, the children are our future."

Cancer Sufferer Demands Euthanasia Bill

Dorothy and her family are campaigning for a "Dying with Dignity" bill, to change this situation. She implores the government to legalize euthanasia.

Reclaim The Streets!

# "People are sick of dirty, smelly automobiles," said protest organizer Jazz Hamilton. "They're choking the city, the environment--our lives! Cars must be banned!"

# "The only thing people are sick of is long-haired idiots riding their bicycles at two miles an hour on major thoroughfares," says committed motorist Bill Li. "People shouldn't be able to protest like this. The government needs to crack down on them."

# The Automotive Manufacturers Association, meanwhile, has called for government support. "It's clear that we need to boost the level of automobile support in this country. This protest this morning is a clear indication of... um... anyway, we need more government funds."

This is the position your government is preparing to adopt.

Appointment Of Spiritual Advisor

It's time for the government to hire a new religious advisor. Your people have narrowed down the candidates to:

1. Catholic Archbishop Stephanie Shiomi: boasts an excellent track record, having rapidly increased church attendances in his constituencies through the "Reaching God Through Guilt" program. Seen as a solid choice.

This is the position your government is preparing to adopt.

2. New Age thinker Abraham Washington: a left-field candidate with some radical ideas. "For me, it's not about the name of your religion. It's about discovering your spirituality in whatever guise that takes. Some people call that a cult: I call it taking spirituality to the people."

3. Finally, there's Jazz Wu. "If I am awarded the appointment, I will immediately resign," the ex-schoolteacher has declared. "Because, frankly, God is a big load of hokey. I'll be doing everyone a favor by just shutting up about it."

The Very Fast Swimmers of Breaststroke is a massive, environmentally stunning nation, renowned for its complete absence of social welfare. Its compassionate, cynical population of 1.829 billion are ruled by a mostly-benevolent dictator, who grants the populace the freedom to live their own lives but watches carefully for anyone to slip up.

The large government juggles the competing demands of Law & Order, Religion & Spirituality, and Public Transport. The average income tax rate is 26%, but much higher for the wealthy. A small private sector is dominated by the Gambling industry.

Citizens frequently whisper of the Internet as 'the domain of the devil', a niche industry catering to S&M enthusiasts has sprung up, private business has started paving paradises and putting up parking lots, and shanty towns are forming in the suburbs of major cities. Crime is moderate. Breaststroke's national animal is the swimmer, which frolics freely in the nation's many lush forests, and its currency is the yen.

Breaststroke is ranked 12th in the region and 67,790th in the world for Highest Average Tax Rates.

YAY I'M NOT SO EVIL VILE & CRUEL ANYMORE!!!

Economic Collapse Looms!

Big business, fed up with over-regulation in Dymanite_go_BOOM, are heading offshore in ever-increasing numbers.

1. "Good riddance!" says noted environmentalist Anne-Marie Wall. "Sniff that air! It's never been so clean! At last, our society is freeing itself from the consumer death-trap! I say it's time to take the final step and outlaw capitalism once and for all!"

2. "This is a catastrophe waiting to happen," says the Chamber of Commerce. "Think of the consequences! Without big business, where do the jobs come from? Where do we get our medicine? Our cars? Our latest fashions? There are dozens of useless regulations the government could abolish today to make life easier for commerce, and it's high time they did."

This is the position your government is preparing to adopt.

The Allied States of Theta Shaowei
"The less we know, the longer the explanation."

UN Category: Democratic Socialists
Civil Rights: Very Good
Economy: Good
Political Freedoms: Good

Location: Funcia
Regional Influence: Minnow

The Allied States of Theta Shaowei is a very large, safe nation, notable for its burgeoning lemming population. Its compassionate population of 172 million are fiercely patriotic and enjoy great social equality; they tend to view other, more capitalist countries as somewhat immoral and corrupt.

The enormous government juggles the competing demands of Commerce, Social Welfare, and Healthcare. The average income tax rate is 38%, but much higher for the wealthy. A small but healthy private sector is dominated by the Information Technology industry.

Schoolchildren have twice-weekly sex education classes, graffiti artists spend lengthy periods of time in jail, midnight raids drag couples from their homes in the name of decency, and [b]the military frequently holds bake sales to raise funds[/b]. Crime -- especially youth-related -- is well under control, thanks to a well-funded police force and progressive social policies in education and welfare. Theta Shaowei's national animal is the lemming, which frolics freely in the nation's many lush forests, and its currency is the shaowei mark.

Theta Shaowei is ranked 5th in the region and 40,315th in the world for Safest Nations.

[quote]midnight raids drag couples from their homes in the name of decency[/quote]

i really don't know where this came from. really. i have never brought that law. but they haven't mentioned that i  allowed all kinds of human cloning programs and genetic reaserches. i don't mine uranium deposits.

[quote="mustafa"]funcia, I think you are spending too much time on the "domain of the devil" if you have 1.829 people in your nation[/quote]

no i'm not
in fact i go on usually only to check my nation or watch lectures or go on this site!

which reminds me of a tip: if you only want large population set your nation to vacation(or if you are busy...and don't anticipate going on....)

but anyway they had a vote on if HarryPotter was evil in my nation...and of course it isn't so the children of Breaststroke are allowed to read....

Minorities Demand Representation in TV Soaps

Dymanite_go_BOOM's TV soaps--famous around the region--have come under fire for their lack of ethnic diversity.

1. "Every night my family and I sit down to watch 'The Brash and the Backstabbing'," says Clint Hanover. "But where are the Liliputians like myself? Where are the Bigtopians? The Marche Noirians? People from those cultures can be just as brash and backstabbing, but we never see them on the screen. The government must act to remove this silent apartheid from our TV screens."

2. "Those Liliputians don't know how good they have it," says Gregory Wong, spokesperson for the Tasmanians Against Ethnic Stereotyping. "Tasmanians are on television all the time, but always in crude, stereotypical roles. The answer is not to enforce ethnic quotas, but to award government prizes for the positive portrayal of minorities. That'll work better, and be cheaper, too."

3. "The government should do what now?" says TV studio executive Roxanne Steele. "You've got to be kidding. We make soaps here, not documentaries. I should be able to put whichever characters I want into my shows. Quotas! Government prizes! God save me! Hasn't the government got anything better to do? Why don't they just back off and let society work out these things on its own?"

This is the position your government is preparing to adopt.

Nudists Demand Time In Sun

A loose coalition of sartorially-challenged individuals known as "Let It All Hang Out" has called on the government to relax public nudity laws.

1. "For too long, our bodies have been trapped in these prisons of cotton and polyester!" yelled protester Fleur Chicago, while apparently developing a nasty case of sunburn. "We must repeal the puritanical laws that make public nudity a crime. My body--my choice to dangle!"

2. "I agree," mused sociology professor Miranda Mombota. "But I don't think the protestors are going far enough. Public nudity shouldn't be an option: it should be compulsory. Nudity is highly liberating. And it would put that disgusting "Hooters" out of business once and for all."

3. "Whoa, whoa," says noted accountant Max Fellow. "Are these people serious? The last thing I want to see when I'm out for a coffee is some lumbering, over-weight nudist coming down the sidewalk toward me. If people want to get naked, they can do it in the privacy of their own homes. Think of the children!"

This is the position your government is preparing to adopt.

Right Of Way Or Wrong Of Way?

The Issue

An increasing number of land owners have been fencing off footpaths which run through or near their property and as a result you have been petitioned by The Rambler's and Hiker's Association to allow the 'right to roam'.

1. Roger Bush, a famous hiker of Dymanite_go_BOOM's countryside, storms into your office, arms waving dangerously. "These pompous land owners are fencing off hundreds of years of tradition! The public should have right of way by law! It is every man's right to be able to enjoy the scenic beauty of our native lands and I don't see why some toffee-nosed prat should be the only person allowed to walk around his hundreds of acres of land when most of us don't even have one! It's simply unforgivable! Now, if you'll excuse me, I'm going for a walk! Wherever I ruddy well like!"

2. "It's trespass, plain and simple," says Gregory Hanover, wealthy owner of six mansions. "My home is my castle! If these smelly ramblers think they can abuse and defile my land, they should start thinking again! You've got to look at this reasonably: where people go, pollution follows. Before I know it I'm going to have litter in my fields, drunken parties in my woods, and more eroded footpaths than I can count! Will they be the ones paying to have it all maintained? Not likely! I say no to this 'right to roam' rubbish! This land is mine, and I intend to keep it that way."

3. "There's an opportunity in every problem," says Clint King, your Minister of Rural Affairs. "And there's always some sort of compromise. We could simply allocate some government funding to teams of environmental workers to maintain and promote our network of footpaths that anyone may use... for a price. Think of the money we could get from all those hikers and ramblers! Not to mention the tourists, birdwatchers, and hippies! Everybody wins! Except for those who can't afford the fees, I guess, but you can't please everyone."

This is the position your government is preparing to adopt.

Animal Liberation Front Strikes Again

The Issue

The increasingly militant Animal Liberation Front struck again last night, freeing dozens of chickens bound for delicious snack packs.

1. "These nuts have got to be stopped," demands concerned consumer Buy du Pont. "They need to face the fact people want snack packs, no matter how many innocent chickens must be sacrificed. Besides, chickens would do the same to us if they had the chance."

2. "These Liberationists are highlighting an important issue," pleads George W. Hendrikson. "Too often, animals are put through needless cruelty, just to make their flesh taste a little more deliciously succulent. I'm sure we could ban the more horrific abuses without putting too much of a dent in our national obesity figures. Couldn't we?"

3. "Animals have feelings too!" yelled protestor Falala Love, before being set upon by hungry passers-by. "Free the animals! Ban meat-eating!"

4. Economist Gregory Broadside has an alternative. "You don't need to take away the people's right to choose. You just need to build the costs of animal suffering into the price. A tax on meat-eating, in proportion to the amount of cruelty involved, would do the trick. Plus think of the benefit for the national coffers! Of course, poor people wouldn't be able to afford meat, but that's just more incentive for them to get jobs."

This is the position your government is preparing to adopt.

Affirmative Action in Dymanite_go_BOOM?
The Issue

After a recent high-profile case of a minority student being refused admission to a traditional, prestigous college, civil rights activists, conservatives, and teachers are up in arms about affirmative action and ethnic equality in education.
The Debate

   1. "This is just another attempt to discriminate against people of color," declares civil-rights activist, former TV commentator and unabashed publicity speaker Buy Licorish. "If people are disadvantaged in their upbringing they they should be given an 'equal' chance to succeed in college."
      [Accept]

   2. "The affirmative action programs aren't necessary at all," rejoins conservative speaker and hair care product salesman Samuel Spirit. "If you really want to treat everyone equally, as you claim, how can you support special treatment for a few so-called minority groups? Besides, it would cost even more money to enforce."

      This is the position your government is preparing to adopt.

   3. "I think you are both looney," says Steffan Rifkin, professor of liberal arts at Dymanite_go_BOOM National University. "All education should be open to everyone regardless of their grades in high school, economic status or academic prowess. Free college education should be available to every citizen of Dymanite_go_BOOM, no matter what the cost!"
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Put The "Board" Back In Board Of Education
The Issue

The Dymanite_go_BOOM Teachers' Union, complaining of a steady increase in student disciplinary problems, wants to be able to use corporal punishment to correct misbehavior.
The Debate

   1. "Clearly, parents aren't teaching manners at home," says Falala Shiomi, the union president. "All we want is to be able to take a paddle to their backsides when there are problems. It's not like we want to throw the kids in jail."
      [Accept]

   2. "Keep your hands off my kids!" shouts Freddy Love, while protesting outside of union headquarters. "If there's a problem, it's with the teachers not having the skills to do their jobs. They should be tested for qualifications!"

      This is the position your government is preparing to adopt.

   3. "Corporal punishment would only treat a symptom of the bigger problem: our education system is in need of an overhaul," says Abraham McAlpin, Dymanite_go_BOOM's education minister. "We need smaller class sizes, more teachers, better buildings, and better pay. It'll cost, but it'll pay off in the long run."
      [Accept]

   4. "Why don't we just abolish the schools and home-school the kids?" asks Stephanie Rifkin, education coordinator for the Dymanite_go_BOOM First Omnimenical Church. "That way parents can stress the values they want their kids to have and give them the attention they need."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Hackles Raised Over Fur Clothes Debate
The Issue

Several animal rights groups have protested the continuing use of fur as a material for clothing.
The Debate

   1. "This is an outrage!" cries Max Johnson, president of the Be Nice To Animals society. "The manufacture of fur apparel is unethical, cruel, and disgusting! People just don't seem to realise that millions of animals die each year in fur farms, crammed into tiny cages and suffering the most terrible treatment just so someone can look appealing and rich! This is a sick practice and must be stopped! The same can go for leather shoes and snakeskin belts too."
      [Accept]

   2. "You can't mean that, surely?" snorts Freddy Longbottom, adjusting his hat, made from real human hide. "It's the people's choice what they wear. I don't think it's fair that the majority of the public should be deprived of fur clothes because some people are a bit queasy. In fact, if the government would allow us to stock rarer animals, we could produce even finer products. In the end, it's up to the consumer, don't you think?"
      [Accept]

The Government Position

The government is preparing to dismiss this issue.

Maternity Leave A Must, Say Mothers
The Issue

A coalition of expectant mothers (Mothers 4 Justice) has banded together to demand legislation allowing for six months of fully paid maternity leave.
The Debate

   1. "Six months?! Six WHOLE months?!" blusters Freddy Rubin, a payroll manager. "Six whole months of being fully paid by our company for doing nothing but looking after a baby?! This will sink the small businesses and lose us an obscene amount of revenue! We cannot allow this to pass!"

      This is the position your government is preparing to adopt.

   2. "I believe that passing this law will be a step in the right direction," says Beth Broadside, the nation's most outspoken feminist advocate. "These kids need their mothers' love and attention during an important part of their growth development! I don't see why mums should be forced to juggle with the stress of bringing up children and having a job! It's simply too much! Six months maternity leave with full pay is what this country needs - even if it is at the expense of a few avaricious fat cats."
      [Accept]

   3. "Look, I've got an idea," says Roxanne Jones, an obsessive centrist. "Perhaps we can allow for six months of paid maternity leave, but have the government pay the companies for lost revenue? That way the mothers can bring up their children without financial worries, companies won't lose investors, and everyone will be happy. Apart from the taxpayers, of course, but you can't please everyone."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 1.

UN Category: Democratic Socialists
Civil Rights: Good
Economy: Good
Political Freedoms: Very Good

UN Category: Corporate Police State
Civil Rights: Some
Economy: Powerhouse
Political Freedoms: Outlawed

The Armed Republic of Asian communists of KS is a large, safe nation, renowned for its barren, inhospitable landscape. Its compassionate, hard-working, cynical population of 26 million are ruled with an iron fist by the corrupt, dictatorship government, which oppresses anyone who isn't on the board of a Fortune 500 company. Large corporations tend to be above the law, and use their financial clout to gain ever-increasing government benefits at the expense of the poor and unemployed.

It is difficult to tell where the omnipresent, corrupt government stops and the rest of society begins, but it concentrates mainly on Social Welfare, although Defence and Commerce are on the agenda. Citizens pay a flat income tax of 59%. Private enterprise is illegal, but for those in the know there is a slick and highly efficient black market in Automobile Manufacturing.

Political activists are routinely executed, the government is avowedly atheist, scenic mountain valleys are flooded with water as damming projects get underway, and eight year-olds with lemonade stands have been known to be locked up on charges of embezzlement. Crime -- especially youth-related -- is totally unknown, thanks to a well-funded police force and progressive social policies in education and welfare. Asian communists of KS's national animal is the fetus, which teeters on the brink of extinction due to widespread deforestation, and its currency is the stem cell.

Asian communists of KS is ranked 5035th in the region and 82,631st in the world for Most Rebellious Youth.

Animal Experimentation Laws Under Scrutiny
The Issue

Scientists and animal rights activists have once again brought up the debate over animal experimentation to your attention.
The Debate

   1. "What have those poor, defenceless animals ever done to us?" asks Jazz Dredd, owner of the East Dymanite_go_BOOM human Sanctuary. "Kidnapping these helpless creatures from their habitat simply to stick probes and needles in them is just barbaric! How would you like it if someone caged you in a lab and conducted tests on you just to find out whether a new product was fit for sale? Experimenting on animals ought to be banned!"

   2. "It is not unethical," replies Dr. Falala Wu, the chief surgeon at Dymanite_go_BOOM's largest Cancer Research Clinic. "The unethical thing to do would be to deny the public of the benefit of the great scientific advancements we're making! If we have to sacrifice some animals in the name of science, healthcare, or a commerical venture, then that's just what we've got to do! Think of the lives we could save! All we require is more government support and funding for this worthy cause."

      This is the position your government is preparing to adopt.

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Sacramental Tax Time?
The Issue

Secularists have been urging for the government to impose an income tax on religious organizations in Dymanite_go_BOOM for some time now, and the issue has finally made it's way to the upper levels of the government.
The Debate

   1. Self-appointed civil rights spokesman Bill Rifkin declares, "Churches are business organizations with a large income. It's unfair that they don't have to pay the same taxes that everyone else does. If they really do spend on any money on charity, let them write it off as a deduction just like corporations do. There's no reason that so-called clergy should be chauffeured around in limos tax-free, when we desperately need funds for public works."

      This is the position your government is preparing to adopt.

   2. "Freedom of conscience is foremost among liberties," says Reverend Alexei King. "Churches have been exempted from taxation because it is wrong for the government to infringe on the right of people to worship as they please, and that includes charging them for the right to worship. Besides, churches are non-profit organizations that put all their funds back into the community."
      [Accept]

   3. The Honorable Sue-Ann Wu, Minister of Minding Other People's Business, has an idea: "This religion thing is such a great racket, why don't we make it a government monopoly? We'll ban all religions except the Church of Dymanite_go_BOOM, and make attendance and donations compulsory. I'll start writing the Holy Scriptures right away!"
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 1.

Licence To Breed?
Government Acts
The Issue

Increasing reports of child abuse and neglect in Dymanite_go_BOOM has prompted local pressure groups to call for 'parental licences'.
The Debate

   1. "You need a licence to keep humans or drive a car," points out local current affairs commentator, Buffy Hendrikson. "So why should just any random idiot get to be a mother or father? It just doesn't make sense! If all potential parents had to pass tests to prove they're responsible enough, I'm sure you'd find that it would help decrease the level of child abuse, and increase proper discipline in the home."
      [Accept]

   2. "This is madness!" screams Miranda Li. "You can't deny perfectly good people the right to bring life into this world! humans manage it easily enough, and you can't tell me they've got more responsibility than your average upstanding citizen of Dymanite_go_BOOM! The government should keep out of such matters - I've always said social workers and welfare was a drain on the budget. Yes, there will be some sad cases of neglect, but shouldn't we be giving parents the benefit of the doubt?"

      This is the position your government is preparing to adopt.

   3. "The answer to this problem is patently obvious," says Zeke Spirit, your minister of Social Welfare. "The government simply needs to give more funding to the welfare department so that we can recruit more social workers to carry out regular checks on parents and judge whether or not they're doing a good job of looking after their children. It'll be expensive, but at least it's a damn sight fairer than licensing parents."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

can u take over other nations in this game?

only regions  :lol:  there used to be a big one that attacked us small regions but they had some probs with leadership i haven't seen them in a while...we have i forget(i can check) who as allies who promised they'd help if we were attacked!

[quote="mustafa"]I got bored being nice, so I am going to become a tyrannical dictator now.

My first act as dictator, KILL THE POETS![/quote]

lol and the artists other than the "art of problem solving" artists  :wink:

[quote]The Issue
A recent, well-publicized UFO sighting over rural areas of Theta Shaowei has turned people's attention to the skies, and what... or who... might be up there.

The Debate
"This event proves one thing: there are other life-forms out there," says eccentric astronomer Fleur Dredd, "All we have to do is find them! What is the price of a few hundred Radio Telescopes compared to the benefit of living in peace and harmony with our brethren of the stars?"
[Accept]

[i]"Spies! It's gotta be spies! A few planes or satellites from our enemies or 'allies' in our region," rages General Jack Shiomi, head of Theta Shaowei's military, "The only way to keep those snoops out of our airspace is to patrol the streets 'n skies, and shoot 'em down! Even if they are some sort of little green aliens, a couple of SAM batteries and a few flak cannons'll [b]keep 'em from abducting our lemmings.[/b]"
[Accept][/i]

"Extraterrestrial lifeforms? Alien invaders? I don't know why we even have to listen to such idiocy!" complains prize-winning physicist Zeke Mistletoe. "In my opinion, the idea of 'aliens' on another planet is highly unlikely, and even if they did exist, getting from there to here is technically impossible! I say we forget this nonsense and stop spending our tax shaowei marks on it. Leave this sort of foolishness to the people who attend those 'trekkie' conventions."
[Accept][/quote]

lol. lemming is our (theta showei's) national animal

Licence To Breed?
Government Acts
The Issue

Increasing reports of child abuse and neglect in Dymanite_go_BOOM has prompted local pressure groups to call for 'parental licences'.
The Debate

   1. "You need a licence to keep humans or drive a car," points out local current affairs commentator, Buffy Hendrikson. "So why should just any random idiot get to be a mother or father? It just doesn't make sense! If all potential parents had to pass tests to prove they're responsible enough, I'm sure you'd find that it would help decrease the level of child abuse, and increase proper discipline in the home."
      [Accept]

   2. "This is madness!" screams Miranda Li. "You can't deny perfectly good people the right to bring life into this world! humans manage it easily enough, and you can't tell me they've got more responsibility than your average upstanding citizen of Dymanite_go_BOOM! The government should keep out of such matters - I've always said social workers and welfare was a drain on the budget. Yes, there will be some sad cases of neglect, but shouldn't we be giving parents the benefit of the doubt?"

      This is the position your government is preparing to adopt.

   3. "The answer to this problem is patently obvious," says Zeke Spirit, your minister of Social Welfare. "The government simply needs to give more funding to the welfare department so that we can recruit more social workers to carry out regular checks on parents and judge whether or not they're doing a good job of looking after their children. It'll be expensive, but at least it's a damn sight fairer than licensing parents."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Prisoners Demand Elbow Room
The Issue

In a display of unity that can best be described as "highly unnerving," criminals and law enforcement officials alike are up in arms about recent overcrowding within prisons in Dymanite_go_BOOM.
The Debate

   1. "I tell ya, chief... this ain't good," mutters local police chief Konrad Barry over his morning cup of coffee. "I see these no-good mohawk-wearin' punks every day, and they're a dangerous bunch. They gotta be locked in their mudholes forever! If we can't afford to keep 'em in prison, I say we need more money! Let's just casually shift some funding from elsewhere; after all, it ain't like our welfare program is helping keep these kids away from crime."
      [Accept]

   2. "How can these wayward individuals find their inner selves by staring at the walls within a stone cell?" challenges human rights activist and local prison license plate maker Buy Falopian. "The nation's budget is absolute proof: we cannot afford prisons... strictly because of their immorality! Let these caged birds breathe the sweet air of freedom again! Shut down all prisons in Dymanite_go_BOOM!"
      [Accept]

   3. "Now hold on just a second here," says Tobias Fellow, CEO of Dymanite_go_BOOM's most widely-known pizza delivery chain, Papa Pallocci's Pizza Pagoda. "You've got a problem with prisoners, and I've got a problem finding employees. Why don't you just send some of your criminals to Papa Pallocci's? We'll put 'em to work at lower pay as punishment for their crimes! I win, you win... the economy wins!"

      This is the position your government is preparing to adopt.

The Government Position

The government has indicated its intention to follow the recommendations of Option 3.

Refugees Want To Call Dymanite_go_BOOM Home
Government Acts
The Issue

After several bloody conflicts in nearby regions, a stream of asylum-seekers and refugees has been spotted heading for Dymanite_go_BOOM's shores.
The Debate

   1. "Some of these people have endured terrible hardships to reach our borders," says International Red Cross spokesperson Fleur Rubin. "We must welcome these unfortunates with open arms. Let the world see that Dymanite_go_BOOM does not turn its back on those in need!"
      [Accept]

   2. "These grasping freeloaders will swamp our culture and traditions!" argues talk-radio host Randy Dredd. "First they want welfare, next thing you know they're taking our jobs -- and you know they won't bother to learn our language. I say charity begins at home -- and this isn't their home. This is the world's problem, not ours."
      [Accept]

   3. Economics Professor Jazz du Pont offers an alternative. "There is no question that we have to help those who reach out to us in their darkest hour. But on the other hand, we cannot help everybody. So let's just take the ones who are willing to keep our streets clean and our drains flowing in return for a subsistence wage."

      This is the position your government is preparing to adopt.

The Government Position

The government has indicated its intention to follow the recommendations of Option 3.

Dymanite_go_BOOM Plagued By STD Epidemic!
Government Acts
The Issue

A medical report has detailed a twenty-fold increase in infection rates over the past ten years of the sexually transmitted disease VODAIS (Viral Overactive Dysfunction of the Auto-Immune System). People all over the nation are petitioning that the government do something about the epidemic.
The Debate

   1. "This situation is about to explode. At this rate, this epidemic could severely impact our economy, our way of life, and even our government," says Doctor Freddy Licorish. "We must supply powerful drugs to all infected people, even if we have to produce and distribute it ourselves. We must also educate people on the dangers of VODAIS and supply condoms to all sexually active males. Sure, we'll need to divert tax money from the military to fund all this, but what good is a military if the soldiers are too sick to fight?"

      This is the position your government is preparing to adopt.

   2. "If you supply condoms, you'll increase sexual promiscuity," scoffs religious leader Jean-Paul Rubin. "If you supply drugs, you'll risk creating an aura of invincibility which in turn increases sexual promiscuity. Sexual abstinence is 100% effective in preventing VODAIS infection. This knowledge must be taught at all schools and workplaces, and all other choices must be ridiculed. Make celibacy the only option!"
      [Accept]

   3. "Supplying drugs and condoms will not stop VODAIS infections and forcing everyone to be celibate will be the slow death of Dymanite_go_BOOM," whispers Health Minister Thomas Shiomi in a poorly-lit back room. "Segregating the infected people is the most effective method. Everybody in Dymanite_go_BOOM must be tested for VODAIS. Then all the VODAIS positive people will be shipped to seperate gated communities away from the rest of us. If they need to mingle with uninfected people, then they must wear distinguishing badges that feature a Grim Reaper holding a skeletal human."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 1.

The Debate
"Although it is often dismissed as an irrelevant complaint, depression is a real disease, it isn't just 'all in your head'," says Naki Spirit, depression sufferer. "Depression has significant effects on groups and individuals, especially amongst teenagers. Every day, more and more people commit suicide because of this disease, but this could all be stopped if this country had a decent level of funding for support and public awareness programs."
[Accept]

"Screw them," Bill O'Bannon, talkback radio host, stated yesterday. "Depression isn't a disease, it's just another example of today's youth finding something to complain about. Life's never been better. In fact, just yesterday, I bought my fourth BMW. And even if it is as serious as the bleeding hearts claim, then I say we leave it and cut some of the funding being wasted on these head cases. If a few whiners jump off a bridge, it'll be good for the genepool. Natural selection, my friends. It's a great thing."

This is the position your government is preparing to adopt.

"Actually, a lot of depression cases in teens are related to school and all the stress and pressure young people are under to succeed. A greater effort to correct the problem of depression should start there, with more funding so that schools can provide better counseling programs." Comments Dr. Beth Bush, author of the book "Tomato Soup for the Soul". "That way teens who are depressed can get help even if their parents can't or won't take them to see a psychologist."
[Accept]
The Government Position
The government has indicated its intention to follow the recommendations of Option 2.

[color=blue]i wasn't sure what to do but didn't care so screw them[/color]

"This is an outrage!" cries Tobias Utopia, president of the Be Nice To Animals society. "The manufacture of fur apparel is unethical, cruel, and disgusting! People just don't seem to realise that millions of animals die each year in fur farms, crammed into tiny cages and suffering the most terrible treatment just so someone can look appealing and rich! This is a sick practice and must be stopped! The same can go for leather shoes and snakeskin belts too."
[Accept]

"You can't mean that, surely?" snorts Bianca Falopian, adjusting his hat, made from real swimmer hide. "It's the people's choice what they wear. I don't think it's fair that the majority of the public should be deprived of fur clothes because some people are a bit queasy. In fact, if the government would allow us to stock rarer animals, we could produce even finer products. In the end, it's up to the consumer, don't you think?"

My new goal is just to take away all rights and get as strong an economy as possible.

Give The Red Light District The Green Light?
Government Acts
The Issue

After a recent survey discovered that nearly 40% of all citizens in Dymanite_go_BOOM are single, there has been an increasingly loud call for the legalisation of prostitution.
The Debate

   1. "I just can't get a girl no matter what I do," laments acne-afflicted nerd, Alexei Silk. "If the cops would just look the other way about prostitution, it'd make my life much easier. Yeah, I'd be risking all sorts of diseases, but it's my body isn't it?"
      [Accept]

   2. "We can't allow this to happen!" protests Dr. Jean-Paul Dredd, senior pathologist of Dymanite_go_BOOM's largest hospital. "Prostitution is a dangerous business and must remain illegal! People need to be more aware of the consequences that could follow like the risk of contracting HIV, chlamydia, or even syphilis. I say we get some funding for a large awareness programme on sexually transmitted diseases and maybe then people will act responsibly between the covers. It'll be expensive sure, but well worth it."
      [Accept]

   3. "Not so fast now!" interjects daring entrepreneur, Hope Wong. "Why don't we just have the prostitution industry run by the government? By letting the government regulate prostitution, Dymanite_go_BOOM can force any patrons to undergo tests for diseases, make prostitutes have regular medical check-ups and pay a portion of their profits to the government. Of course we'd still have to put more policemen on the streets to keep illegal brothels from popping up and make sure the hospitals are equipped to handle the extra workload, but you can always raise taxes to account for that."

      This is the position your government is preparing to adopt.

The Government Position

The government has indicated its intention to follow the recommendations of Option 3.

Karate Kids Cause Controversy
Government Acts
The Issue

Free, youth-orientated martial arts programmes have gained popularity in communities where youth crime is a problem.
The Debate

   1. "What better way to keep kids off of the streets?" asks Charles Wong, a professional judo instructor. "It's fun, good exercise and gives an invaluable insight into our nation's culture! It gives these youngsters something positive to channel their energy into; energy that might have otherwise been used to rob banks or mug people in alleyways. But self-defence programmes like mine will need government funding to really make a difference - surely the public wouldn't mind paying a little more tax to put an end to the gangs of yobs prowling the streets?"
      [Accept]

   2. "It's a good idea, but it's not taking it far enough!" declares General Steffan Licorish of Dymanite_go_BOOM's army. "If we could conscript these kids into the army, we'd be able to put their skills to good use! No one would mess with Dymanite_go_BOOM if we had a butt-kickin' karate unit on the battlefield! It may be a little expensive but we can just take money out of the education budget since these kids will be under our tuition. Their families may not be happy about it, but remember this: these young lads will be getting to do something which is the envy of every hot-blooded citizen - fight for their country against blood-sucking foreigners!"

      This is the position your government is preparing to adopt.

   3. "This is ridiculous!" comments police officer, Faith Christmas. "Teach junior thugs how to fight? Good idea, why don't we teach them how to make bombs out of duct-tape and cheese next? I say we ban this archaic mode of combat which only serves to encourage these punks in their violent ways, and introduce more government funding for the police force! With more cash we could really show the little blighters what discipline's all about."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Scandal Rocks Dymanite_go_BOOM's Government!
Government Acts
The Issue

A tabloid magazine, The National Incriminator, has revealed the sordid details of an affair between one of your top advisors, Robert Lotsalovin, and his secretary.
The Debate

   1. "They found out I did WHAT?!" Advisor Lotsalovin says in his morning meeting in your office. "This just can't happen! How can government officials do their jobs properly if we have to work under the constant scrutiny of these idiotic supermarket tabloids? I say tabloid newspapers must be banned, and we must not allow newspapers to speak ill of our government officials... for the good of Dymanite_go_BOOM, of course..."

      This is the position your government is preparing to adopt.

   2. "Unbelievable!" says Reverend Lars Li of the local Catholic church. "Our government officials must be held to a higher standard than this! Mr. Lotsalovin must be removed from office and jailed. We cannot allow such disgusting corruption within the halls of justice!"
      [Accept]

   3. "Whoa, whoa, hey, now..." argues Senator Pip du Pont. "What happened to Mr. Lotsalovin is no different than affairs that happen all over Dymanite_go_BOOM every day! Before you know it, they'll be after YOUR sexual history! I think what we need to do is take the public attention off of it somehow, perhaps by... oh, I don't know... giving them a tax cut! That'll divert their attention from this momentary distraction just long enough for Mr. Lotsalovin's divorce process to end!"
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 1.

Dymanite_go_BOOM Looks to the Stars
Government Acts
The Issue

The recent popularity of a science-fiction TV show has prompted calls for Dymanite_go_BOOM to develop its own space program.
The Debate

   1. "Don't tell me space colonies wouldn't be cool," says excited fifth-grade teacher Beth O'Bannon, still wearing big Spock ears from his last convention. "Think of how they would galvanize the national population! And there would also be some kind of scientific benefit, probably."
      [Accept]

   2. "The project certainly is feasible, but very expensive," says Dymanite_go_BOOM Space Agency Head Faith Gutenberg. "We could make it less of a burden on the taxpayers if we sought funding from private industry -- advertisements on the side of our rockets, selling contracts to the Arms Manufacturing industry, that kind of thing."

      This is the position your government is preparing to adopt.

   3. "If God had meant Man to fly, he would have given us solid rocket boosters instead of legs," says religious type Charles Washington. "We should not be looking to the stars, but rather inside our own hearts. That's why we should abandon this so-called space program, and instead make the teaching of religion mandatory in all schools."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 2.

Genetics Brings New Life to Extinct Species
Government Acts
The Issue

Scientists have announced they are close to a breakthrough in their quest to revive the feather-bellied human, a species related to Dymanite_go_BOOM's national animal that has been extinct for more than a century.
The Debate

   1. "I, for one, applaud their work," says scientist Anne-Marie Li. "And not just because I'm the project leader. This is an example of how Dymanite_go_BOOM's brains can mix it with the world's best. Can you imagine how wonderful it will be to have feather-bellied humans frolicking in the meadows again? I say full steam ahead, and more government funding!"

      This is the position your government is preparing to adopt.

   2. "This is a sacrilege!", says religious leader Thomas Love. "These animals are extinct because God wants them dead. Cloning them would merely incur his wrath! If we proceed down this path, it'll be humans, not the feather-bellied human, who will be extinct."
      [Accept]

   3. "Now, come on," says Chastity Spirit, well-known philosopher. "You don't need to be religious to be unnerved by the top of this particular slippery slope. Today it's humans, tomorrow it's dinosaurs, and we all know how that turns out. This research shouldn't be banned, but there must be strict government controls over its use."
      [Accept]

The Government Position

The government has indicated its intention to follow the recommendations of Option 1.

A coalition of tribalists, health experts, and civil rights proponents have recently suggested legalizing cannibalism for consumers of willing would-be meals.

The Debate
"I see absolutely no problem with people digging into each other at dinnertime, so long as everyone is willing," Konrad Clinton, the editor of the monthly magazine 'To Serve Man', quips, "Not only does it solve hunger problems and create jobs, but it also adds variety to Breaststroke's sometimes dull palette."
[Accept]

Civil rights leader Violet Longbottom came out publicly for moderate pro-cannibalism legislation, commenting, "While it may strike some as a crude, even evil practice, our ancestors have practiced cannibalism for years. If we create a government organization to strictly regulate and grade all human meat prior to its arrival on the market, we can ensure that respect for diversity is maintained while health concerns are also allayed. And instead of killing average people, why not make being turned into snack foods a post-mortem option? Like donating your body to science!"
[Accept]

"You're all absolutely out of your minds!" exclaims Jennifer Rifkin, head of Breaststroke's largest health-food manufacturer. "It's immoral, it's unhealthy, and it's disgusting. Not only are these so-called 'dietary rights' activists leading us down a dark path of sin, but right into a marketplace with yet another product that's almost as bad as beef!"

This is the position your government is preparing to adopt.
The Government Position


Let $ a,b$ be positive integers such that $ a^n\plus{}n|b^n\plus{}n$ for all natural number $ n$
show that $ a\equal{}b$


If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is about H(x) = 20 - 4.9x^2. When does the rock strike the ground?

Does the rock strike the ground when x = 0?

Do I plug 0 for x and simplify?

Any tips?

You should plug in 0 for H(x), not x. Plugging a 0 in for x would give the height of the rock at 0 seconds, or 20 ft. Plugging in a number for H(x) makes you solve for the time it takes to get to that height.

[hide="It should look like this"]
$0 = 20-4.9x^{2}$
$4.9x^{2}= 20$
[/hide]

I thank you for the tip.

I can now solve for x.

x^2 = 20/4.9

x = 2.02 seconds.


function articles Harvard college topology

Why do the Chinese teams score so marvelously on competitions such as the IMO, but do they somehow fail to become famous as professional mathematicians? I know very little chinese (or asian in general) famous mathematicians.

How comes?

Don't they join the western research community?

One should really expect that China delivers fine mathematicians daily :)

I'm just interested. Hopeful someone can answer my question :)

I think a big reason is that the training is SO intense. The stereotypical Asian (or Chinese) - American parent drilling kids in homework, extracurriculars is magnified over there. I think a lot of the kids are trained from a young age, exclusively. They become somewhat of "problem solving machines". Although they are so brilliant, they might not have the vision to become great research mathematicians. Also, there might not even be that big of a connection between success at problem solving and becoming a famous (or historically great) mathematician, although I do believe it certainly helps a lot. Another reason could be that they choose to pursue careers other than research. With the great problem solving skills, it shouldn't be too hard for them to earn large sums of money (not that you can't as a professor.......)

This is kind of off topic, but I heard there is also some controversy regarding the state of math in major universities in China involving yao...

[quote="Jacobson"]Why do the Chinese teams score so marvelously on competitions such as the IMO, but do they somehow fail to become famous as professional mathematicians? I know very little chinese (or asian in general) famous mathematicians.

How comes?
[/quote]

That's easy. Being a mathematician isn't exactly the highest paying job that world can offer and although it is very interesting, that's pretty much the only benefit.

Actually being a mathematician can deliver good pay, but none of the jobs that do that seem to be open.

There have been a good number of influential Chinese mathematicians in the past fifty years or so (although I am not sure of any correlation between them and the Chinese IMO team). I would be most inclined to go with the "they only learn how to do amazing brute-force computations and memorize tons of techniques so they aren't actually that good at research" and "they take industry jobs instead of professorships because they're better jobs, especially in China" theories.

(Note that a lot of good Chinese mathematicians got their college degrees in the West. This is probably because China is still trying to get its university education to the level of Western institutions. In Chinese culture, doing theoretical research is not as highly regarded as in Western culture, I think. Westerners have a kind of reverence for "theory" that we can't understand [possibly because we are accustomed to that with religion], and the Chinese are not as much like that.)

First, I'd point out that the "ideal system" for producing IMO gold medalists is probably very different from the "ideal system" for producing research mathematicians.  Just as both are very different from the "ideal system" for producing a mathematically literate populace.  In other words, I don't think that the correlation between IMO performance and research output should be all that large.

Second, the basic premise is wrong.  There ARE lots of good Chinese mathematicians.  Most of them work in the United States.  Peruse the faculty lists at top universities, and you are bound to see Chinese surnames, and most of them are NOT Chinese-Americans. (Chinese-American mathematicians are actually rare.)

Third, I don't know how long China has been doing well on the IMO, but I imagine it hasn't been more than 30 years.  Keeping in mind that most "famous" mathematicians are in their 60's or older, they were in high school a long long time ago, so this could account for why there are so few "famous" Chinese mathematicians.  In particular, the Cultural Revolution pretty much decimated the Chinese educational system for many years.

Fourth, in a developing country, becoming a mathematician is a less popular career choice.  For example, if you are poor and good at math, the obvious way out of poverty is to become an engineer rather than a mathematician.  Some other posters touched on this topic.

In any case, no one doubts that Chinese mathematicians are bound to have a greater role in the world of mathematics in the coming years.

[quote]In other words, I don't think that the correlation between IMO performance and research output should be all that large. [/quote]
So, what is the function of IMO? I think it is to find the young mathematician all over the world to make a betterment to the world.

actually in pretty much eveything academics, asians rule at tests and stuff, that's cause they were trained from when they were in only 5, a first grader in china has more homework than a 6th grader here. and in highschools, they have to wake up at 5 in the morning class ends 9p.m. almost all students live in the school, so each week they gave them only 1 hour to play, and the rest of the time, including weekends, they devote to intense studies.(that one hour they get is to take a bath each week).
most parents want their kids to be rich in asia, so they usually tell them to pursue better paying jobs, and after more than a decade of memorizing,( a first grader has to memorize a whole essay at least once a week) brainwashing( mostly communist ideas and how bad the west are...) and brutal treatment(if a  students whisper in class the teacher will probably smack their head against the wall really hard,), i doubt they will do good at pure math careers.

[quote="krustyteklown"]
This is kind of off topic, but I heard there is also some controversy regarding the state of math in major universities in China involving yao...[/quote]

Let me clear up this part of the discussion. A magazine published an article full of lies that was discrediting Shing-Tung Yau (who is still a professor at Harvard), and my dad, a former postdoc of Yau, who has written several papers with him, is working on this with him (and a lawyer, I presume). But the controversy was started by the magazine, and Yau was not dishonest in any way, as the article seems to convey.

Well, if you mean The New Yorker's "Manifold Destiny", I am inclined to believe that their description was accurate in every essential detail. I understand that it hurts Yau and may be quite unpleasant for his friends, but I don't doubt he is no saint. His speech about the role of Chinese mathematicians in the proof is no hoax and that alone would be enough to accuse him of an attempt to steal the credit for the proof from Perelman.      So, I don't think he stands any chance in his "legal battle" with New Yorker. I'm not 100% sure whether it was this particular story that was behind Perelman's decision to quit mathematics, but if it was, Yau is guilty of much more than a theft attempt: I would then incriminate him with "professional murder" of one of the most brilliant problem solvers. Also, in my humble opinion, the right way for a mathematician of his rank and talent to clear his reputation after what happened is to work not with lawyers but with chalk and blackboard and to prove something equivalent in value to the proof of Poincare conjecture ;) As you might guess, I don't know Yau personally, but I used to know Perelman fairly well, so I felt obliged to respond to your "clarification" :)

On the other hand, I doubt that Yau's or anyone else's personal honesty or lack of such has anything to do with the general state of the Chinese educational system so I also do not see why one should mix the two in one sentence.


OK, I will be hosting another math jam.
It will be either sunday evening/night, or some weekday evening/night, since I have Spring Break.
I would be happy to host two before next Saturday.
If you are interested and did not attend the math jam today, please leave me your screen name in some way.
Also, anyone interested, please respond HERE regarding when you can meet Sunday evening/night, and which weekday evening/night you would be able to participate in.
I will be posting the official rules here, since that took about 20 minutes today.

Assume that all math jams will be about an hour long, starting between 7 and 8 EST.

i can do sunday.
about this week, i can only do it if it is 700 est or later (o yeah it is)

i can do sunday too. evening is probably the best time for me.

I can do it on Sunday. Around 8 P.M. would be great.

OK then.
I have tentatively scheduled an AIM math jam for Sunday evening, about 7:45 EST to 9 EST.
Participants:

-Pianoforte*
-Biffanddoc*
-Goldenomer*
-Kyyuanmathcount*
-nonie*
-slamchess*
-lucy4eva*
-easyas3.14159...*
-noneoftheabove*
-ccy*
-xxmorgo74xx*
-zenith xan*
-dark knight*

A * indicates that I know this user's AIM screen name. If your username does not have a *, please tell me your screen name.

Feel free to invite anyone you know interested. Freshman are allowed, but no one older, please.
I probably won't be on tomorrow, but if I am, it'll be around 4-5 EST. If I am on then, I will write a brief explanation of my system thing.

Wait... what is this for?

I might be attending.

Screenname: (this was a long time ago)=>  poopyloopy2003

I should be able to---I'm not sure though.

[hide="aim"]asinglespark1[/hide]

[quote="kyyuanmathcount"]
Screenname: (this was a long time ago)=>  poopyloopy2003[/quote]

 :rotfl:  :rotfl:
are you serious?

i've already been to state, but it was fun watching last time. so if i'm on at that time, can you just invite me? thanks.

[hide]luver of rain[/hide]

[quote="Klebian"]OK, I will add you guys to the buddy list.
Also,
ATTENTION: The time for tomorrow's AIM math jam type thing has been changed.
Due to conflict of schedule, I will be moving it half an hour later (Sorry Easterners)
It will be from 8:15 to 9:15 or 9:30 EST.
If you are unable to attend the whole thing, that is fine.
I know this is a bit late, but its the only way I can get it into my schedule.

This was meant to be a kind of State preparation, but its just countdown type problems, kinda fun for anyone who attends.
I've also developed a fairly efficient system for making the whole thing work.
Please be on by 8:10 or so to get the rules, as the system will need explaining.[/quote]was it the same system as last time?

Yes, but some people weren't here last time.

I could make it.

[hide]insanemorgoth[/hide]

I can probably make it.

My SN is below (the AIM button).


inequalities
algebra
polynomial
inequalities unsolved

Thanks for that. Unfortunately, I typed the wrong inequality! The correct should be
\[\frac{l-k}{\sqrt{1+15kl}}+\frac{k-1}{\sqrt{l^{2}+15k}}+\frac{1-l}{\sqrt{k^{2}+15l}}\geq 0. \]
with $k\geq l \geq 1$. $k=8,l=7$ is not a counterexample anymore.

Now I found something. The inequality is equivalent to
$(k-1)/\sqrt{l^{2}+15k}\geq (k-l)/\sqrt{1+15kl}+(l-1)/\sqrt{k^{2}+15l}.$
Since all terms are known to be $\geq 0$, this inequality holds iff the
squared inequality
$(k-1)^{2}/(l^{2}+15k) \geq  (k-l)^{2}/(1+15kl)+2(k-l)(l-1)/\sqrt{(1+15kl)(k^{2}+15l)}+(l-1)^{2}/(k^{2}+15l)$
holds.
This is equivalent to
$(k-1)^{2}/(l^{2}+15k)-(k-l)^{2}/(1+15kl)-(l-1)^{2}/(k^{2}+15l) \geq  2(k-l)(l-1)/\sqrt{(1+15kl)(k^{2}+15l)}$
and this is true iff the left hand side is $\geq 0$ and the squared
inequality holds.

The squared inequality holds because by Maple

factor(((k-1)^2/(l^2+15*k)-((k-l)^2/(1+15*k*l))-(l-1)^2/(k^2+15*l))^2-(2*(k-l)*(l-1))^2/((1+15*k*l)*(k^2+15*l)));

gives

$(l-1)^{2}\cdot (k-1)^{2}\cdot (k-l)^{2}\cdot \text{huge}/((l^{2}+15\cdot k)^{2}\cdot (1+15\cdot k\cdot l)^{2}\cdot (k^{2}+15\cdot l)^{2})$

wher huge is a polynomial with respect to $k$ and $l$ and with positive coefficients. So if one proves
\[(k-1)^{2}/(l^{2}+15k)-(k-l)^{2}/(1+15kl)-(l-1)^{2}/(k^{2}+15l)\geq 0,\]
the inequality is proven.


In how many different ways can a panel of four on-off switches be set if no two adjacent switches may be off?

[hide]

Sometimes it's easier just to count the choices.

There are 2:^4: ways of setting the lights, but in half of them, two or more adjacent lights are off. Answer is 8.

[/hide]

[quote]but in half of them, two or more adjacent lights are off.[/quote]

How do you know that?

Is there a way to prove that? (Prove that half of all possibilities have at least two adjacent switches off)

Yeah, I was looking for a general proof.

Well...it could be a general [b]dis[/b]proof :wink:  :wink:

I dunno realli...i think counting's much easier in simple cases like this...if it was 50 switches for example, id be interested in finding a rule...

in any case, theres 5 ways for 2 and only 2 off switches to be adja.
2 for 3 off switches to be adj.
and 1 for all 4 to be off (duh!)

Right, if N meant "on" and F meant "off"
FFNN
NFFN
NNFF
FNFF
FFNF

FFFN
NFFF

FFFF
is possible, total of 8.

but i guess...we're still looking for a generalization...

Yeah that may not work in general. However there is a nice formula for n lights..

Here is a suggestion for tackling the generalization for n switches:

Imagine each off switch not as its own switch, but as an off switch that is necessarily attached to an on switch on its right.

The only place where this doesn't help is an off switch located on the far-right end.

Even with this suggestion however this generalization problem belongs in the intermediate area of the forum.  This is more like a Masters Round problem at National MATHCOUNTS -- far more involved than any regular MATHCOUNTS problem.


function
combinatorics proposed
combinatorics

Consider a finite alphabet A. An infinite word w (with letters from A) is said u-periodic if it is of the following form:w=abbb..bb...
where the words a and b are finite.

let W be an arbitray infinite word with letters from A. Define $F_n$ be the number of subwords of length n of W (s is a subwords of gst where g,s,t are words )
Define $F_n$ be the number of distinct subwords of W of length n. Then prove the following fact:
($n->F_n$ is a bounded function) i.e. (W is u-periodic)

You catch me!!! ;)

I thought whole 15 minutes!  :)

Of course, it is very simple! I'll wait until someone else solve it. I don't want to deprive other problem solvers pleasure of solving this problem...  :D

Wow! We left this unsolved for wuite some time, didn't we? :)

Assume $n\mapsto F_n$ is bounded.

Since $F_n$ is increasing (for each distinct subword of length $n$, there is a distinct subword of length $n+1$ beginning with the subword of length $n$) and bounded, it must be constant from some point on. Consider $n$ large enough that $F_{2n}=F_n$. The conclusion easily follows: each subword of length $n$ is uniquely determined by the preceding subword of length $n$ (because $F_{2n}=F_n\Rightarrow$for each subword $a$ of length $n$, there is precisely one subword of length $2n$ beginning with $a$), and, since there are finitely many subwords of length $n$, this sequence eventually becomes periodic.

The other implication is easy :).


The following one is not at all a difficult inequality, but I like the form it has: total irregularity:
   Prove that for all x,y,z>0 with x+y+z=x^3+y^3+z^3 we have:
    (z/y)^2*x/(x^2+1)+(x/z)^2*y/(y^2+1)+(y/x)^2*z/(z^2+1)>=(x+y+z)/2.

This very nice inequality is too much difficult for me.
Have you a solution , Harazi?

Thank you very much.

The following solution is quite artificial, but it's neat (I see that everyone likes this word). All we have to do is to observe that multiplying the LHS with sum x(x^2+1) and applying Cauchy-Schwartz we will find that the result is at least ( xy/z+yz/x+xz/y)^2. It can be easily proved that xy/z+yz/x+xz/y>=x+y+z. Taking into acount that sum x(x^2+1)=2sum x, we obtain exactly the desired inequality. I remeber to have found another solution to this problem, but I don't remeber it now.

Very nice solution. It's the solution that you remember for long time. The idea of using Sum (x+x^3) = 2Sum(x) is so suprising (and after reading it becomes so natural!). The idea of using C-B-S is wellknown and you see, very effective in manipulation with such "ugly" expression. Thank you Harazi for submitting this nice solution.

Namdung


By law of cosines:
$c^2=a^2+b^2-2ab\cos{C}$
so $c=\sqrt{a^2+b^2-2ab\cos{C}}$
by triangle inequality $a+b>c$

It's a little easier than that.

The maximum value of the left side occurs when $C = 180^{\circ}, \cos C = -1 \implies \sqrt{a^2 + b^2 - 2ab \cos C} = a + b$.  For every other value of $C$, you can see that $a^2 + b^2 - 2ab \cos C < a^2 + b^2 + 2ab = (a+b)^2$, giving us the desired result, with equality at $C = 180^{\circ}$.

[quote="breez"]In a triangle, the sum of the length of sides $a$ and $b$ is always greater than the length of side $c$.

Based on the truth of this statement,

$\sqrt{a^2 + b^2 - 2abcosC} \leq a + b$ for $0^\circ \leq C \leq 180^\circ$

Prove this statement true.[/quote]

It should actually be strict, or you get a degenerate triangle; you can form the other side of the inequality to get

$|a-b| < \sqrt{a^2+b^2-2ab\cos{C}} < a+b$ for $0<C<180$.


A chocolate bar is in the shape of an equilateral triangular prism. Each edge of the base is 1 inch, and the length of the bar is 8 inches. What is the number of cubic inches in the volume of the bar? Express your answer in simplest radical form.

u find the area of the triangular base which is 1*1/2sqrt3 divided by 2 so...

1/4sqrt3

then u multiply by the height which is 8.

2sqrt3


Hi

I was wondering if anyone knows where I can find the 2008 Chinese Girls Math Olympiad?

Thanks

http://www.mathlinks.ro/resources.php?c=37&cid=148&year=2008
As you with.


induction
Euler
combinatorics proposed
combinatorics

This is very easy, but I found it kind of cute :).

We divide the surface of the convex polygon $P_0P_1\ldots P_n$ into $n-1$ triangles by drawing $n-2$ non-intersecting diagonals. Prove that the triangles can be labeled $T_1,\ldots,T_{n-1}$ s.t. $T_i$ contains the point $P_i$ for all $i\in\overline{1,n-1}$.

It is easy to prove there is a vertex with no diagonal drawn from it (by induction, or by eulers formula i think, or suming angles, anyway many ways) so remove the triangle formed by a diagonal 2 sides of the original poligon and that contains that vertex. Say that vertex is $n$, so number this triangle $T_n$, and remove it. Do induction now... :)

ooops i think i have some mistakes, actually there are two of such special triangles, also by induction, so one of them has a vertex different from $n$, we can ignore it and do induction,am I understanding it right?

Yes, I believe you're right. Another way to see that there must be two special triangles, as you have defined them: the dual graph of the triangulation is a tree, and the triangles corresponding to the vertices of degree $1$ are special triangles (and it's well-known that every tree has at least two vertices of degree $1$).

I did something a bit different: Label the triangle $P_0P_nP_k$ with $k$, and continue by induction on the remaining figure.


does anyone have it?

if so, do you recommend it

it looks pretty cool and its the only one that can run halo 2 on PC!!! :D

Yeah, it has nice graphics, but before saying anything about it, it has to be said that Microsoft recommends 2gb RAM (!!!) to make it work properly.

It takes up something like 15 GB of hard drive, or so I ve heard.  I don t suggest going to it just yet.  One thing I don t like is that Office 2007 documents, if saved using the automatic file format, wont be able to be opened unless you have Office 2007 (until programmers figure out how to make emacs, for example, to open them).  The main improvements in Vista seem to be just some bells  and whistles added on and the security.  I don t really know in what ways the security is better or how much this will impact the average person, but they claim it s much better.  So if security is a big thing for you, then Vista would be much more preferable to XP.

Make sure Vista is supporting your hardwares. I've seen one person installing it and realizing that his sound card isn't supported (yet).

I have some friends with it. They say it's good for everything. EVen with the big space, their comps are so good that they can still download limewire videos and stuff... weird

Vista does look pretty good, but only compared to previous windows....
Look at linux  :lol:
[url]http://www.beryl-project.org/features.php[/url]
[url]http://www.go-compiz.org/index.php?title=Video[/url]

GO LINUX!!!

Don't buy vista. If you liek graphics, get Vista Transformer pack.

If you're gonna try installing your own OS for the first time, try installing Ubuntu before you go buy your Vista, and see if it isn't sufficient for your needs.

If you're a Windows user and you're getting ready to dismiss all of these suggestions of "try Linux," check this out: you don't need to take Windows off your computer to try out Linux. That is, you could still use your computer just like you used to, and then you could switch it over to Linux and play with that when you had free time. Then if you liked Linux enough, you could just get rid of the Windows part (preferably after salvaging all of your useful data).

Google "dual boot" or check out the software by [url=http://www.vmware.com/]vmware[/url]. (Wikipedia has a [url=http://en.wikipedia.org/wiki/VMware]page[/url] on vmware too.) It's worth trying!

Or even better...try Virtual PC.

Then you install it on your Windows Virtual PC and you can see Linux when you want to.

And if you like it better, then just put Linux on your HD and remove teh Windows Partion

@solafidefarms: SuSE not Ubuntu :D

[quote="joml88"]I've asked a few people what their suggestion was for Linux distribution and I've gotten Ubuntu each time.  I'm still running Windows...eventually I'll get Linux going.  Have to back my files up first...[/quote]
The point of my post was that you don't have to back everything up and abandon Windows. :P You can just partition your HD, leave everything you already had as it was, and put your distribution of choice on the other space. Then either you have one of this virtual box programs that makes your computer think it has another computer inside of it, or you dual boot. (Well I guess if your HD is full, you need to make some room for the other OS, though...)

As for distributions, my most respected Linux geek friend suggested Ubuntu or Fedora Core. He uses the latter, so I'll probably do that, but that's mainly because he's a good friend of mine and I can ask him for help.

What's up iwht Fedora?

Suse can do more stuff. :wink:

Yes, I plan on partitioning my hard drive and dual booting.  And [i]that[/i]'s why I plan on backing my data up first.  Not to mention I should have my files backed up anyway... :ninja:

[quote="#H34N1"]@solafidefarms: SuSE not Ubuntu :D[/quote]
I don't want to argue about the merits of linuces (:lol:), but I don't like SuSE because it's kinda slow, weird, and difficult. I like Ubuntu because it's easy and featureful. But I personally use Gentoo when I have any choice; the only reason I have a Ubuntu machine is that Gentoo wouldn't "just work" like Ubuntu would, and I didn't have time to make it work. (I have 3.5 Gentoo machines: the family computer is a dual-boot between G and the only Windows in the house.)

One of my other good friends likes Gentoo (and he also always has trouble getting it running, especially with the wireless card). I always hear Ubuntu as the "easy" or "intro" Linux, but most people who have time to spend with their computers tend to move on to (presumably more complicated) things.

I like how this topic has shifted to the relative merits of Linux distributions.  But as long as we're there, I might as well ask: what distrib do you guys recommend for a longtime Windows user to use on a rather old computer [350 MHz Pentium II, 96 MB RAM, 9GB hard drive, 8 MB graphics card, dial-up internet] ?  I've tried Red Hat, but it took up over half of the hard drive so I reinstalled Windows 98.
Thanks.

Back on topic, I'm going to studiously ignore Vista.  The new features seem to be largely eye-candy, some seem poached from Mac OS X (Spotlight, for example), and because it's supposed to be so resource-intensive.  There's also the question of price - I'm not going to spend a lot of money to get a new OS when the old one works well and there's not a compelling reason to upgrade.

Just my $\$$0.02 .

i tried windows vista rc1 for about 2 weeks. from my experiences, it was very buggy. internet explorer frequently had problems and few of my applications could run as they did on xp. so, im not even touching vista until sp1 comes out. =)

[quote="Danbert"]I like how this topic has shifted to the relative merits of Linux distributions.  But as long as we're there, I might as well ask: what distrib do you guys recommend for a longtime Windows user to use on a rather old computer [350 MHz Pentium II, 96 MB RAM, 9GB hard drive, 8 MB graphics card, dial-up internet] ?  I've tried Red Hat, but it took up over half of the hard drive so I reinstalled Windows 98.
Thanks.[/quote]

Xubuntu might be what you're looking for. You'll have a hard time doing a lot with those specs, but recently I installed Xubuntu on a system similar to yours, also Win98 originally. It had a smaller hard drive but faster proc (2.2G HD, 630MHz PIII). http://www.xubuntu.org/get#requirements But you're going to have a really, really, really long wait to download any Linux...

@Xev: Gentoo is for people who like tinkering with their systems or want the very fastest system possible. The wireless isn't always that bad, it depends on the wireless card. I have a broadcom card and while I can't use the default kernel sources it is easy to get the required drivers for it. Ubuntu can be as complicated as you want, but it's probably never going to be as fast as Gentoo or Arch.

[quote="Danbert"]Thanks for the reply.  I can download some ISOs at school, as long as I've got a long study hall and a fast download speed, but that's limited because there's a draconian firewall that blocks file downloads based on MIME types - even ZIP files and tarballs are blocked, but application/octet-stream is not, so I can get ISOs with that MIME type.  Unfortunately, that seems to be the minority.

  I do have a Gentoo LiveCD that doesn't even load (too little RAM, I assume, as it works on my other, far newer computer), and ordered Solaris 10 (which definitely won't work) and Ubuntu (which probably won't) discs from Ubuntu's [url=http://shipit.ubuntu.com]ShipIt[/url] program and Sun's equivalent program.  I'm beginning to suspect the Solaris install disc will never come, though - it was supposed to take 10 business days, and I ordered it about a month ago.[/quote]

You aren't going to have any LiveCD load; you'll need to do a text-based install, whatever distro you use.

Your Solaris disk hasn't come because the Solaris CD service got slashdotted. Mine has taken just as long. As for your ubuntu cd's, a cd in hand is worth 10 in the mail :); from what I remember, it'll be a while before your ubuntu cd's come.

@solafidefarms:  Actually, I found a really old Knoppix livecd that loads.  Ha!  True, KDE doesn't work normally - but I can use a swapfile to help.    The Ubuntu CDs were supposed to take 4-6 weeks to come, putting their arrival in mid to late February, but that service was probably slashdotted as well.

@#H34N1:  Because I can only download disc images at school, I can only get ISOs that have MIME type application/octet-stream (not application/x-isoview or some other type) and high transfer speed (because I have a maximum time on the computers of 1hr 15m).  This severely limits the distributions I can get; Ubuntu wouldn't download, so I decided I might as well have a CD or two for free.  The same goes for Solaris.  It's free! Why not?

I'll try Xubuntu (again?) Tuesday when I have free time.


calculus
integration
inequalities
limit
logarithms
real analysis
real analysis solved

Evaluate

\[\lim_{x\to\infty}\frac{\ln x}{x}\int^x_{ e^3}\frac{dt}{\ln t}\]

L'Hospital's rule is in order here.

$\lim_{x\to\infty}\frac{\int_{e^3}^x\frac{dt}{\ln t}}{\frac{x}{\ln x}} = \lim_{x\to\infty} \frac{\frac1{\ln x}}{\frac 1{\ln x}-\frac1{\ln^2x}} = \lim_{x\to\infty} \frac1{1-\frac1{\ln x}}=1$


modular arithmetic
abstract algebra
superior algebra
superior algebra unsolved

Let $ n$ be a positive integer, which can be written $ n\equal{}n_1n_2$ where $ n_2, n_2$ are integers $ \geq 2$ and relatively prime. Show that there is an isomorphism

$ f: \mathbb{Z}/n\mathbb{Z}\to \mathbb{Z}/n_1\mathbb{Z} \times \mathbb{Z}/n_2\mathbb{Z}$

where the map $ f$ associates to each residue class $ a\pmod{n\mathbb{Z}}$ the pair of classes

$ a\pmod {n\mathbb{Z}}\to (a\pmod {n_1\mathbb{Z}}, a\pmod {n_2\mathbb{Z}}).$

everything besides the surjectivity is obvious. choose integers $ u,v$ such that $ u_1 n_1 \plus{} u_2 n_2 \equal{} 1$. now construct an inverse map.

I recommend not constructing an inverse map, but calculating the kernel.

yeah the kernel is trivially zero .. ok the surjectivity follows then by a counting argument, which does not work in the general context ;)


calculus
integration
trigonometry
limit
complex analysis
algebra
partial fractions

Hi, I was wondering if anyone can solve this integral without using Fourier transforms.  Thanks.

Question:  Evaluate $ \displaystyle\int_0^{\infty}\frac{u\sin tu}{1\plus{}u^2}du$, $ t>0$.

First, define:

$ F(t)\equal{}\int^\infty _0 \frac{u \sin tu}{1\plus{}u^2}\,du$

We can see that:

$ F(t)\equal{}\int^\infty _0 \frac{1}{u}\frac{(u^2\plus{}1\minus{}1) \sin tu}{1\plus{}u^2}\,du\equal{}\int^\infty _0 \frac{1}{u}\frac{(u^2\plus{}1) \sin tu\minus{}\sin tu}{1\plus{}u^2}\,du \equal{}$

$ \equal{} \int^\infty _0 \frac{\sin tu}{u}\,du\minus{}\int^\infty _0\frac{\sin tu}{u\left(1\plus{}u^2\right)}\,du\equal{}\frac{\pi}{2}\minus{}\int^\infty _0\frac{\sin tu}{u\left(1\plus{}u^2\right)}\,du \, , \quad t \geq 0$

Now we have:

$ F''(t)\equal{}\minus{}\frac{d^2}{dt^2}\int^\infty _0\frac{\sin tu}{u\left(1\plus{}u^2\right)}\,du\equal{}\int^\infty _0\frac{u \sin tu}{1\plus{}u^2}\,du\equal{}F(t)$

Solving this differential equation is easy, and we get:

$ F(t)\equal{}C_1 e^t \plus{} C_2 e^{\minus{}t}$

And we have:

$ F(0)\equal{}C_1\plus{}C_2$

$ F'(0)\equal{}C_1\minus{}C_2$

So, we need to find initial conditions. We have:

$ F(0)\equal{}\int^\infty _0 \frac{u \sin 0}{1\plus{}u^2}\,du \equal{} 0$

$ F'(0)\equal{}\frac{d}{dt}\left(\frac{\pi}{2}\minus{}\int^\infty _0\frac{\sin tu}{u\left(1\plus{}u^2\right)}\,du\right)\equal{}\minus{}\int^\infty _0\frac{1}{1\plus{}u^2}\,du \equal{} \minus{}\frac{\pi}{2}$

From this we have:

$ C_1\equal{}\minus{}\frac{\pi}{4}$

$ C_2\equal{}\frac{\pi}{4}$

So finally:

$ F(t)\equal{}\minus{}\frac{\pi}{4} e^t \plus{} \frac{\pi}{4} e^{\minus{}t}\equal{}\minus{}\frac{\pi}{2}\sinh t$

There's an immediately visible problem with that solution. We should have $ F(t)\to 0$ as $ t\to\infty,$ and you don't have that - you have $ |F(t)|\to\infty.$ This has to be wrong.

That method relies on manipulating all sorts of integrals that aren't absolutely convergent, which means that various things can slip through the cracks. In this case, it's that $ F$ isn't continuous at zero; we have that $ F(0)\equal{}0$, but not that $ \lim_{t\to 0^\plus{}}F(t)\equal{}0$.

Complex analysis: First, note that $ \frac{u\sin tu}{1\plus{}u^2}$ is even in $ u$. Redefine $ F(t)\equal{}\frac12\int_{\minus{}\infty}^{\infty}\frac{u\sin tu}{1\plus{}u^2}\,du\equal{}\frac1{2i}\int_{\minus{}\infty}^{\infty}\frac{ue^{itu}}{1\plus{}u^2}$

Now, we evaluate this by the residue theorem. For $ t>0$, complete to a closed contour with a big semicircle in the upper half-plane. The integral around the semicircle goes to zero, so $ F(t)\equal{}\frac1{2i}(2\pi ir(t,i))$, where $ r(t,i)$ is the residue at the one pole $ i$. The residue of $ \frac{ue^{itu}}{(u\plus{}i)(u\minus{}i)}$ at $ i$ is $ \frac{i\cdot e^{i^2t}}{2i}\equal{}\frac12e^{\minus{}t}$, and thus $ F(t)\equal{}\frac{\pi}{2}e^{\minus{}t}$.
For $ t<0$, we do the same in the lower half plane. Since we're traversing in the opposite order, signs reverse and we get $ F(t)\equal{}\frac1{2i}(\minus{}2\pi i r(t,\minus{}i))\equal{}\minus{}\pi\cdot \frac{\minus{}ie^{i(\minus{}i)t}}{\minus{}2i}\equal{}\minus{}\frac{\pi}{2}e^t$

The answer in one expression: $ F(t)\equal{}\begin{cases}\frac{\pi}{2}e^{\minus{}|t|}&t>0\\0&t\equal{}0\\\minus{}\frac{\pi}{2}e^{\minus{}|t|}&t<0\end{cases}$

Thank you for the replies.  I have found a way to do this too by Laplace Transforms.

Begin with $ \displaystyle f(t)\equal{}\int_0^{\infty}\frac{u\sin tu}{u^2\plus{}a^2}du$ where $ a,t>0$.
Take the Laplace Transform of both sides, $ \displaystyle F(s)\equal{}\int_0^{\infty}e^{\minus{}st}\int_0^{\infty}\frac{u\sin tu}{u^2\plus{}a^2}dudt\equal{}\int_0^{\infty}\frac{u^2}{(u^2\plus{}a^2)(s^2\plus{}u^2)}du$
By partial fractions, $ \displaystyle F(s)\equal{}\frac{s^2}{s^2\minus{}a^2}\int_0^{\infty}\frac{1}{u^2\plus{}s^2}du\minus{}\frac{a^2}{s^2\minus{}a^2}\int_0^{\infty}\frac{1}{u^2\plus{}a^2}du$
Thus, $ \displaystyle F(s)\equal{}\frac{s}{s^2\minus{}a^2}\left(\frac{\pi}{2}\right)\minus{}\frac{a}{s^2\minus{}a^2}\left(\frac{\pi}{2}\right)\equal{}\frac{\pi}{2}\left(\frac{1}{s\plus{}a}\right)$
Taking the inverse Laplace Transform, $ \displaystyle f(t)\equal{}\frac{\pi}{2}e^{\minus{}at}$.

In this problem, $ a\equal{}1$, so the integral is $ \displaystyle\frac{\pi}{2}e^{\minus{}t}$ for $ t>0$.


function induction calculus derivative logarithms inequalities ARML

[hide]Claim: The sequence $a_k$ is bounded above by 4/3 and strictly increasing.

To prove bounded above, the function $X^x$ is increasing because $X>1$. But also $X=(4/3)^\frac{3}{4}<4/3$, so $a_1<4/3$. Then using induction, if $a_k<4/3$, then $X^{a_k}<X^\frac{4}{3}=4/3$.

To prove increasing, calculus can be used. The function $X^x-x$ has a derivative of $X^x \ln X -1=X^{x-1} \ln (4/3)-1$.
When $x<4/3$, $X^{x-1}<\sqrt[3]{4/3}<2$. Since $(4/3)^2=16/9<2<e$, $\ln (4/3)<\frac{1}{2}$. Then $X^{x-1} \ln (4/3)<1$ so the derivative is negative.

Since the derivative is negative, if $x<4/3$, then $X^x-x>X^\frac{4}{3}-4/3=0$. Then $X^x-x>0\Rightarrow X^x>x$.

Then there is the following inequality: $a_5<a_{1000000}<4/3$. Using calculator, it can be shown that $a_6>1.3325$. Since $4/3=1.333\ldots<1.3335$, $a_{1000000}$ rounded to the nearest thousandth must be $\boxed{1.333}$.[/hide]

I don't know of any easier way to be rigorous. Of course, if you just needed the answer, all you would need to know for sequences like these is:

[hide]Suppose $X=L^\frac{1}{L}$ where $L$ is some positive real number less than $e$, $a_1=X$, $a_{n+1}=X^{a_n}$. For large $N$, $a_N$ will be very close to $a_\infty$ which is given by $L$. So knowing that the answer to the above problem was 1.333 was the easy part.

Of course, there is a catch. If $L>e$ then $a_\infty$ won't be $L$, it will instead be $K$ where $0<K<e$ and $K^\frac{1}{K}=L^\frac{1}{L}$.
(If this doesn't make sense at first, look at $L=4$. Here $X=\sqrt[4]{4}=\sqrt{2}$ and $K=2$.)[/hide]

I recognize this from ARML homework...
This was posted barely over a week after that page of problems was assigned...
Citistarz, any chance you are from Western Mass?

[hide]
Let N = the limit of a_n as n -> infinity.
N = [(4/3)^(3/4)]^[(4/3)^(3/4)]^[(4/3)^(3/4)]^[(4/3)^(3/4)]^[(4/3)^(3/4)]^...
By substitution, N = [(4/3)^(3/4)]^N, N = (4/3)^(3N/4) and by inspection, N = 4/3
a_1000000 is likely very close to N, so the answer is 1.333[hide="note"]there are very specific conditions under which the substitution of infinite exponentials work; for example, x^x^x^x^... = 2 can be solved this way, but x^x^x^x^... = 4 gives invalid solutions[/hide][/hide]


Let $ a, b, c %Error. "belong" is a bad command.
to R$
Prove that
$ (ab+bc+ca-1)^2 >= (a^2+1)(b^2+1)(c^2+1)$.

[quote="Aravind Srinivas L"]Let $ a, b, c %Error. "belong" is a bad command.
to R$
Prove that
$ (ab + bc + ca - 1)^2 > = (a^2 + 1)(b^2 + 1)(c^2 + 1)$.[/quote]

I think $ (ab+bc+ca-1)^2\le (a^2+1)(b^2+1)(c^2+1)$.
By expansion, Problem
$ \Leftrightarrow a^2b^2+b^2c^2+c^2a^2+1+2abc(a+b+c)-2(ab+bc+ca)$
$ \le a^2b^2c^2+a^2b^2+b^2c^2+c^2a^2+a^2+b^2+c^2+1$
$ \Leftrightarrow (abc)^2+(a+b+c)^2\ge 2abc(a+b+c)$, It is obvious.

Thats how even i did. But try solving without expanding for most steps :D .


function
inequalities unsolved
inequalities

Find the function f: R->R
[img]http://www.mathlinks.ro/Forum/latexrender/pictures/993290998c538a37c4418be9e0b8608a.gif[/img]

this quite confusing with the parenthesis and with the $y$ and $x$ in the end. is this what u mean?

$f(x^5)-f(y^5)=(x^2+y^2)\left(f(x^3)-f(y^3)+(xy)^2\left(f(x)-f(y)\right)\right)$

this is a double post. Yo'uve already posted it in the algbera section(I think ... correct me if I'm wrong)


What is the sum of the prime numbers less than 10?

Prime numbers mean that it only has 2 factors: 1 and itself.
Testing, get 2,3,5, and 7.
2+3+5+7=5+5+7=10+7=17.

Note that 1 isn't prime, nor composite, since technically it only has one factor, 1.


calculus
integration
function
calculus computations

Hello:

I was wondering if anyone has an idea how to tackle this problem.

Given $f(x)=f(2x) \;\ and \;\ f(x+1)=f(x)+1/3$, find $\int_{0}^{1}f(x)dx$

I was thinking maybe trying $\int_{0}^{1}f(x)dx=F(1)-F(0)$ and so forth, but it went nowhere.

Any ideas?.

Thanks

Are you sure there's not a typo? I don't think such a function exists. When x = 1 the first equation gives f(1) = f(2); whereas the second equation gives f(2) = f(1) + 1/3. This is a contradiction.

I thought something was wacky, but I thought maybe it was me.

Thanks. I will find out if there's a typo.


Let p be a prime of the form 4k+1. p=4k+1

Prove that $\sum_{i=0}^{k}{ floor( \sqrt{ip}) }= \frac{p^{2}-1}{12}$

Thanks.

and here too :
http://www.mathlinks.ro/Forum/viewtopic.php?highlight=polya&t=5928

Pierre.


[quote="frt"]Solve for $x$:

$2\sin^{-1} (x+2)=\cos^{-1} (x+3)$

($\sin^{-1} \alpha=\arcsin\alpha$, $\cos^{-1} \alpha=\arccos\alpha$)[/quote]

RHS lies in $[ 0,\,\,\pi ]$
LHS lies in $[ - \pi ,\,\,\pi ]$

for the equality to happen, $0 \le x + 2 \le 1$

let $\sin ^{ - 1} (x + 2) = \alpha$

so, the given equation can be written as,

$\cos 2\alpha  = x + 3$

$\Rightarrow 1 - 2\sin ^2 \alpha  = x + 3 \Rightarrow 1 - 2(x + 2)^2  = x + 3$

Solving for x, we get $x=-2$  or  $x=-2.5$

But it can be checked that only  $x=-2$ is the solution.

[quote="maokid7"]i haven't tried to solve this problem but i think there is an error in the provided solution.
the RHS lies in [-pi/2, pi/2]
and the LHS lies in [0,pi]

well that was the only mistake i say other wise it looks to be right[/quote]

Range for $\cos ^{ - 1} x$  is  $[0,\,\,\pi ]$ only.  Not  $[ - \frac{\pi }{2},\,\,\frac{\pi }{2}]$.  Please check yourself.

Everything is right with the solution.

oops sorry about that i typed the wrong thing well i meant that arcsin is form -pi/2 to pi/2 and not -pi to pi. that is what i meant to correct you on.

[quote="maokid7"]... well i meant that arcsin is form -pi/2 to pi/2 and not -pi to pi. that is what i meant to correct you on.[/quote]

Agreed.  I wrote LHS, which is two times arcsine,  lies between $[ - \pi ,\,\pi ]$.

o i didnt get that well then i there isnt anything wrong with your answer  :lol:

[quote="krustyteklown"][quote="vidyamanohar"][quote="krustyteklown"]hm how can x+2 equal 1, or be greater than 0, when x+3 is being plugged into inverse cos?[/quote]

 the RHS lies in $[ 0,\,\,\pi ]$ and double the arcsine has to lie in $[ 0,\,\,\pi ]$

that makes $0 \le x + 2 \le 1$ as  the required condition for the equality to happen.  It does not mean that x+2 should/can be equal to one.[/quote]

Yeah, worded kinda strange, taking that fact, and the fact that x+2 has to be smaller than/equal to 0 because x+3 goes into cos, don't you already get x=-2?[/quote]

you are right.


For what ordered pair $ (a,b)$ are there infinite solutions $ (x,y)$ to the system
\begin{align*}
3ax+3y&=5b\\
2x+y&=5
\end{align*}

\begin{align*} 3ax + 3y & = 5b \\
2x + y & = 5 \end{align*}

We need to make the first equation be equivalent to the second equation.  This can simply be achieved by multiplying by a constant--$ 3$.  The second equation becomes:

$ 6x + 3y = 15$

The first equation is $ 3ax + 3y = 5b$.  The equations match if $ a = 2$ and $ b = 3$.  $ \boxed{(2,3)}$


complex numbers
combinatorics proposed
combinatorics

Find the number of ways in which x and y can be selected from the first 25 natura numbers such that x^4-y^4 is divisible by 25.  :P

[hide]$105=5^{2}+4\cdot (5^{2}-5)$
Here $5$ can be replaced by arbitrary prime $p=4k+1$, i.e.
we have $p^{2}+4\cdot (p^{2}-p)$ required pairs $(x,y), \ x, y \in \{1,2,3, ... , p^{2}\}$for a prime of this  kind

For a prime $p=4k-1$ we obtain $p^{2}+2\cdot (p^{2}-p)$ required pairs.
To complete we have $16$ for $p=2$[/hide]

I don't quite understand how u can write the formula directly ...
Can u tell me the process of getting it ??  :maybe:
Thx

The form I've gave the answer was a hint how to count.
Here is
[hide="solution"][b]Let $p=4k+1.$[/b] Then there exist $a$ for which $a^{2}\equiv-1 (mod \ p^{2})$ - in particular take $a=7$ for $p=5$.
Now we have $x^{4}-y^{4}\equiv (x-y)(x+y)(x-ay)(x+ay) (mod \ p^{2})$
[u]Case 1.[/u] Two or more multiples of the last congruence are devisible by $p$. Then abviously $x\equiv y \equiv 0 (mod \ p)$. This gives $p^{2}$ required pairs.
[u]Case 2. [/u] Only one of the multiples is divisible by $p^{2}$. Take arbitrary $y\not\equiv 0 (mod \ p)$ and calculate $x$. This gives $p^{2}-p$ pairs for each multiple of the four. Hence in total we have $p^{2}+4(p^{2}-p)=p(5p-4)$ required pairs.

[b]Let $p=4k-1$[/b]. Then there is no $a$ for which $a^{2}\equiv-1 (mod \ p^{2})$ holds. It follows that $p | x^{2}+y^{2}$ iff $p | x$ and $p | y$. This gives $p^{2}+2(p^{2}-p)=p(3p-2)$ required pairs.

Note. Evident pairs of the kind $(x,x)$ are included here and pairs $(x,y)$ $(y,x)$ were assumed different.
If some other interpretation of "Find the number of ways" was mentioned by [b]ashwinkrishnan[/b] then there is no problem to improve above formulas. [/hide]

cool man I really loved the way you used to simplify x^2+y^2 its like in complex numbers, but in remainder theory everything is okey, very impressive, through I did this problem easily but without this trick. It is really simple thing, right, but I'll come back to this forum with a problem I remembered right now - one very hard, but I think can be solved like this easily:)))

THX