Does anyone really say "line"? I've heard "link", but not that. And "arc" is usually only used in the directed case, in which case you could also throw in "arrow" as an option. I was never taught graph theory formally and neither were my peers, soo... anythin...

Does anyone really say "line"? I've heard "link", but not that. And "arc" is usually only used in the directed case, in which case you could also throw in "arrow" as an option. The different terms for vertices are a legitimate source of disagreement. In my exp...

I often do not trust programs to correctly interpret paths/names with spaces, so I try to put all files that are to be used by a program in a spaceless path. Documents (spreadsheets and stuff) can go where ever. What are you doing with those spreadsheets that doesn't involve them being used by any ...

can handle integers and strings and even arrays. if they are integers, it will add them as expected and return the result. if strings, it will concatenate them and return. if arrays, it will add the elements of the the arrays ([1,2,3]+[4,5,6] = [5,7,9]) This is not correct. While what you wrote arg...

It doesn't work in ZFC, in the same way that defining cardinals as isomorphism classes of sets doesn't work in ZFC. There exist set-theoretic tricks for making sense of this idea, which also work here if this MathOverflow answer is to be believed. If I recall correctly, Conway himself considers the ...

1 Or "Lego" or "LEGO", but never /legos/i. (Sand grains, lego bricks. Pile of sand, sack of lego.) :shock: Careful now. I've been down this road before... It's only the Brits that have this one right. I'm Canadian and was weirded out when I started encountering the assertion tha...

Historically number theory was often referred to as "arithmetic", and occasionally it still is. (This is basically analogous to the way mathematicians use "algebra" and "geometry" to describe branches of mathematics that in their modern incarnations don't have much obvi...

Do cups with fewer person-hours of design and debate tip more or less frequently than those designed in 'haste'? As far as the switch being on the cord, I'd hope that particular lamp is plugged in to a switched outlet. I, personally, wouldn't want a switched cord on a desk lamp where the switch was...

You can't discriminate a number just because it doesn't follow all of the properties the other primes might have. It's practically racist. A platypus is a mammal even though it doesn't have most properties most other mammals have. It is considered a mammal because it fits the basic definition. Biol...

Neither 1 nor -1 has a prime factor, because they are both units. You can't solve a problem by stating a tautology, Nyktos. Everyone knows 1 or -1 is also called a unit. But all prime numbers have 1 or -1 as a factor. As do all numbers (except possibly zero) Yes, all numbers are divisible by 1 and ...

But you still need some restriction there, or you have (-2)*(-3) = 2*3, and 6 no longer has a unique prime factorisation. Meanwhile, -1 has no prime factors at all. Neither 1 nor -1 has a prime factor, because they are both units. 6 already doesn't have a unique factorization, as it is both 2*3 and...

1 is not prime because it is not useful to define it to be prime. If 1 is prime, all the theorems about prime numbers don't start applying to 1, nor do they stop existing all together: they just become theorems about non-unit primes instead. Writing "non-unit prime" all the time is a waste...

I find the power set argument cleaner, especially since you can formulate it in a way that resembles Russell's paradox. If f is a bijection (actually we only need to assume it's a surjection) from X to its power set, the set Y = { x ∈ X : x ∉ f ( x )} must be the image of some point y , and then bot...

I'm curious, tho - why convert to binary? There doesn't seem to be any particular reason to do so, as the construction works just as well in decimal - (123, 5) maps to 102035, and similarly an arbitrary number like 12345 maps to (135, 24). Yeah there's no real reason to use binary actually. I had s...

That's not a bijection, as many of the integers aren't mapped to - in particular, anything with a 0 for its second digit. I don't know what you mean by this. 10 has zero as its second digit, and it's the image of (1, 0). Or did you mean second in the other direction? 101, for instance, is the image...

N 2 is indeed > N, but its still "countable" because N 2 can be contained in a finite number of dimensions of size N (specifically 2). That's not what countable means. Countable means you can literally count it - you can rearrange the set so that there is a natural number corresponding to...

prove that not every irrational number will be on bus 2. i can't accept the standard proof here, because the bus is infinitely long, and contains an infinite number of irrationals all "randomly" generated, so if it differs by 1 decimal place, somewhere else may contain the corrected versi...

I'm gonna say it again: all the completeness axioms are the same for an ordered field. The page you linked claims otherwise. For an ordered field, Cauchy completeness is weaker than the other forms of completeness on this page. But Cauchy completeness and the Archimedean property taken together are...

That metaphor doesn't work. Your photo would obviously appear to everyone to be red. Yes, we could understand that your dress is actually white and merely appears red because red light is being shined on it. But people wouldn't perceive it to be different than the actual RGB values of the image fil...

Right. I could take a picture of a white dress under, say, red light. Undoubtedly if you examined the RGB values of the pixels making up the image of the dress, they would be shades of red or pink. But people would likely have no trouble telling that the dress is actually white, because the human br...

I suspect the puzzle is trying to be a different puzzle entirely where we assume that all references to "The Engineer" and "The Programmer" can refer to any engineer/programmer rather than a specific one and that one of the brothers is both so what appears to be a contradiction ...

Alternatively, you could just create a new class that inherits from the module class -- with x as a @property -- and find a way to create a module with *that* class instead of the standard module class. You can do this with import hooks, though of course for that to work you need to arrange to have...

I would consider that ugly. Sometimes a function returning different types based on the input is reasonable but that usually takes the shape "output type is the same as input type" or something along those lines. In your case I think it would be better to just give class X a different meth...

Nyktos, in C++ variables are names for things. The thing they are a name for never changes (so long as it exists) in its fundamental nature. That thing can be a *pointer* to another thing if you want. A reference is an alternative name for a thing, and similarly what it refers to never changes (so ...

...which makes me think you could use a similar technique to 'jury-rig' constraints on variables (by assigning them to objects that do insidious shit when you try to delete them). Dunno if that would work, though (and it's definitely very unpythonic!). That won't work if you end up with other refer...

I'm not very well versed in C++ so I'll being deferring to your knowledge and expertise on most of that. As far as optional<optional<X>> goes, in all the literature and examples I've seen it could just be flattened to optional<X>. That outer wrapping isn't really serving much purpose. In Rust, iter...

Way back when, I learned that "whole" numbers are {1, 2, ...} and natural numbers are {0, 1, ...}. Or maybe it was the other way around. Maybe I should say "I was taught" instead. :-) I'm certain that in high school I was taught that "whole numbers" include zero and na...