text:
Q: Might the derivative be a measure of a shrinking curve instead of a point? I see a lot of posts here questioning the validity of 'instantaneous rate of change' and most responses point to the epsilon–delta definition of a limit (or at least some informal version of it). My understanding is that with this definition we calculate the average change of a function across some non-zero interval, and then continue to decrease the interval to no end, at least in principle.
Since this process never ends, the object of study is always a curve, not a point. Albeit, it is an ever shrinking curve but it is a curve nonetheless. In one breath we stress that the interval never actually becomes zero, but then in the next breath we claim that the derivative corresponds to the slope of the tangent line at a point. To me this seems to be a contradictory view.
I have a view on this issue for which I would love to hear your criticisms. I argue that the issue stems from us constructing continua from points when we should be constructing points from continua. To explain my view, consider how we draw graphs. We start with a blank piece of paper (a continuum of sorts) and draw lines on it (i.e. axis lines, grid lines, functions, etc.). Only once these lines intersect can we identify points. With this construction, points are emergent, not fundamental. Since we can continue adding lines to no end, we'll never completely fill the paper with ink. There will always be continua in between the lines. Might the derivative describe not the points, but the shrinking continua adjacent to the points?
My apologies if I was unclear in the last paragraph, I provided more details on this view in a YouTube video if you are interested.
I believe that continuum-based constructions don't face the problem of completeness and paradoxes of actual infinity present with point-based constructions. As such, it's a view that I find hard to let go of but I want to let go of it if it's wrong. So I would appreciate it if you can point out problems with this view.
Thanks for your time.

A:
the interval never actually becomes zero, but…slope of the tangent line at a point. To me this seems to be a contradictory view.

If $f$ is differentiable at $a$, then "the tangent line at $a$" or "the tangent line through $a$" refers to a particular line through the point $(a,f(a))$ (specifically, the one with slope $f'(a)$). There's at most one tangent line for each point $(b,f(b))$ on the graph, so we can speak of the tangent line at a point, if it exists. I don't see any problem with this terminology.
I'm not sure, but it seems like you might be objecting to the fact that defining the derivative (the slope of the tangent line) involves secant lines which always pass through two relevant points on the graph. My personal gut reaction is "That's why we don't call it the 'secant' line at the point. The different word 'tangent' is used for that reason."

the issue stems from us constructing continua from points when we should be constructing points from continua.

I'm not certain I understand what you're getting at here, but it seems like your idea might not work well for an example like $f(x)=\begin{cases}x^{2} & \text{if }x\in\mathbb{Q}\\0 & \text{else}\end{cases}$. There are holes in the parabola part of that graph, and it's not anything like a simple contiguous curve near $(0,0)$, but it's still differentiable at $0$ and so most would say it still has a tangent line there.

Since we can continue adding lines to no end, we'll never completely fill the paper with ink.

I'm having trouble understanding what this part of the discussion has to do with the derivatives part, but this depends sensitively on how (or "how fast") we add lines. For example, if I want to fill the unit square with vertical line segments, let's just say I fill $x=0$ through $x=t$ by time $t$, so that by time $0.1$ I've already added a continuum's worth of lines. Then I'll completely fill the square by time $1$.

redpajama_set_name: RedPajamaStackExchange


text:
Sophie Turner Pours One Out For A "Very Good Man"
Kaitlin Reilly
This post contains spoilers for episode 3, season 8 of Game of Thrones.
Sunday's Game of Thrones was a game-changer for the HBO series. While the Battle of Winterfell may not have boasted the deaths of too many main characters (thanks, mostly, to Maisie Williams' badass Arya Stark), the souls who did die on the battlefield gutted us emotionally at the same time the White Walkers gutted them physically. Alfie Allen's Theon Greyjoy lost his fight with the Night King, making for a very emotional moment. Now, Sophie Turner is pouring one out for her fellow GoT cast member, who she only recently reconnected with.
Turner's Sansa Stark got through the Battle of Winterfell relatively unscathed, despite hiding in the crypts which, as it turned out, are a terrible place to seek refuge from dead-raising zombies. Greyjoy wasn't quite so lucky, and it's unlikely we'll be seeing any of Allen's character in GoT's final three episodes.
Turner — who, just last week, took to social media to celebrate the sex scene between Arya and Joe Dempsie's Gendry — couldn't let such a major GoT moment pass without commenting. Turner's last words to her fallen friend, posted on Instagram, echo the words that Bran Stark (Isaac Hempstead Wright) called out to Theon just before Theon rushed towards the Night King.
Where Does GOT Go After That Night King Twist?
What Happened To Melisandre On GOT?
Is Arya Actually Azor Ahai On Game of Thrones?
"To Alfie and to Theon.... 'You're a good man,'" wrote Turner on Instagram.
Fans shared their love for Greyjoy in the comment section. (Well, those fans who weren't complaining about Turner spoiling Sunday's episode.)
"I started crying when Theon was the last one standing protecting Bran," wrote one GoT fan. "And even more so when Bran told Theon, he was a good man."
"The tears when this scene came on! Theon had his ups and his downs but always had a spot with me," added another. "He died being a hero!"
"I'm so sad he died but glad he got the closure he deserved and left the show as an honourable man," said a third fan. "Best character development ever."
However, others questioned whether Theon really deserved such a title.
"Still don't think he fully redeemed himself. He did horrible horrible things," reminded one Instagram commenter. "Yes he did some good as well but I don't think the scales are balanced."
Regardless where we stand on Theon's redemption arc, one thing's certain: Game of Thrones will have many more deaths to cry over in upcoming weeks, now that the gang is taking on Cersei (Lena Headey). Keep your eyes on Turner's Instagram for more memorials.
Sophie Turner Honors Theon Greyjoy Battle Of Winterfell
Entertainment • Game of Thrones • News • TV Shows
written by Kaitlin Reilly

redpajama_set_name: RedPajamaCommonCrawl


text:
These Terms and Conditions for Services (herein referred to as "Terms") are published by CADEAUX GINKGO AG, Metallstrasse 9 B, 6300 Zug, Switzerland (herein referred to as "CADEAUX"), and its associated companies, employees and sales personnel dealing with products of CADEAUX, in particular but not limited to products under the brand name Cadeaux Jewelry.
These Terms apply to servicing (referred to as "service(s)/servicing") of jewelry, watches or other products (referred to as "product/products") owned by individuals or companies (referred to as "customer/customers") and handed to CADEAUX for service, irrespective of whether such products were acquired by the customer from CADEAUX or not.
By using CADEAUX'S services the customer agrees to the Terms herein. Any deviation from these Terms must be agreed on in writing.
CADEAUX reserves the right to modify these Terms, and any such changes take effect when they are posted on this website. It is the customer's obligation to read these Terms when the customer uses CADEAUX'S services.
CADEAUX may carry out services as cleaning, polishing, sizing, repairing, or any other services agreed on. CADEAUX shall only carry out and invoice services that have been based on cost and time estimates and accepted by the customer. CADEAUX enters an obligation to service only when CADEAUX confirms acceptance of a required service in writing with a Service Order (referred to as "Service Order").
Obligations and Cancellation
By placing a Service Order with CADEAUX, the customer enters an obligation to pay for and accept the service being provided, and CADEAUX enters an obligation to carry out the service to the satisfaction of the customer.
Until a Service Order is confirmed, the customer has the right of cancellation at no cost. CADEAUX has the right not to service a product if the price cannot be agreed on with the customer, or for any other reason. CADEAUX has the right to cancel a Service Order after acceptance if for any reason the service cannot be carried out, and in such case the customer is entitled to a full refund of any prepaid service and to the return of the unserviced product.
CADEAUX may publish prices for services. Published prices are not binding on CADEAUX until confirmed in a written Service Order. Prior to confirmation CADEAUX reserves the right to change prices at any time, however, CADEAUX shall not change a price after a Service Order has been confirmed, unless a price change is subsequently agreed on mutually with the customer. Any price offer will be subject to customer's acceptance and the offer will have a validity of 15 days.
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A product is deemed received by CADEAUX when received at an authorized point-of-sale or office of CADEAUX, and when CADEAUX has issued a Repair Receipt. A product is deemed returned to the customer when returned at an authorized point-of-sale or office of CADEAUX, and when CADEAUX has received the original Repair Receipt in return from the customer. A customer's failure to return a Repair Receipt does not mean a product has not been returned to the customer.
On a Repair Receipt CADEAUX records the visual condition of a product, including scratches, dents and damages, plus defects reported by the customer. An initial damage record is not conclusive and CADEAUX may subsequently discover further hidden damages which may not have been visible on initial inspection and may only have been discovered during the process of servicing, and CADEAUX may subsequently inform a customer of such hidden damages accordingly.
Conversely, CADEAUX will accept liability for any service performed beyond the return date of the product to the customer for a period to be specified by CADEAUX and depending on the nature of the service carried out.
A CADEAUX Repair Receipt is provided only to acknowledge receipt of a product and its reported condition and does not entail CADEAUX'S obligation to service a product.
On return of a product to the customer, the customer must check the product on receipt. If the customer thinks there are any defects to the product other than those recorded on the Repair Receipt, or that the product does not correspond to the one originally delivered to CADEAUX, the customer must make an immediate claim in writing. CADEAUX will not accept responsibility for customer claims reported subsequent to delivery. Conversely,
If the customer for any reason refuses to accept the delivery the goods will be stored by CADEAUX at the customer's expense pending acceptance.
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With a Repair Receipt CADEAUX assumes responsibility for the safe-keeping of the product until it is examined, a quotation is made and it is returned to the customer, whether repaired or not. Excluded from CADEAUX'S liability are any losses of products in transit or in safe-keeping if these are caused by force majeure and/or acts of war or riots.
CADEAUX receives and returns products at authorized point-of-sales. Delivery to other locations, as a home, office or hotel, must be agreed on by CADEAUX and noted in the Repair Receipt, and may be subject to extra charges for delivery, shipping and packaging. CADEAUX is not responsible for products, or damages to products, that are delivered to locations not agreed on by CADEAUX.
In case of damage or loss to a customer's product, CADEAUX'S liability is limited to the price the customer paid for the product based on an official receipt presented by the customer to CADEAUX, or to replacing the product by an equivalent one. CADEAUX'S liability is limited to an equivalent of US$ 10,000 (US Dollars ten thousand) per product, unless prior to CADEAUX'S acceptance of the product the customer provides evidence that the customer has paid a higher price and CADEAUX accepts such stated price by writing it on the Repair Receipt. In all cases CADEAUX'S liability will not exceed US$ 30,000 (US Dollars thirty thousand) per product, unless the customer asks for and agrees to pay for insurance exceeding this amount and a written agreement between the customer and CADEAUX is made. Insurance charges will be for the customer's account.
CADEAUX is not liable for any amount higher then the aforementioned, in particular not for perceived, emotional, collector's, vintage or other values, nor for any economic losses, loss of goodwill, or other losses the customer may claim to have suffered as a result of any loss of or damage to a product by CADEAUX.
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Zug, Switzerland, 25th April 2015
CADEAUX GINKGO AG, Metallstrasse 9 B, 6300 Zug, Switzerland
© Copyright 2015. Cadeaux Ginkgo AG. All rights reserved.


by Moishe & Yetta Feiner.
Spanning perhaps the most devastating epoch of all of Jewish History, the lives of this remarkable couple are told here by the protagonists with disarming simplicity and spine-chilling directness. From the beleaguered stetlach of the Ukraine to the snowbound steppes of Siberia, from the awe-inspiring Court of the Holy Tzaddik of Belz to the field kitchens of the Soviet Army, this is a Jewish survival narrative unlike any other that I have ever read or heard. Rife with hair-raising terror and trauma, pathos and hilarity, yet brimming with Holiness, with open Miracles, and with unswerving Faith in G–d, this book is a living, unadorned, historical testimony of what it really means to be a Jew in the last and darkest moments before the Ultimate Redemption.


Why you should shop Pakistani suits from boutique?
A good wardrobe redefines your persona and classic choice. In the fashion evolution there are various dresses for feminine beauty but everything stands out to be fade when it comes to beauty of ethnic wear. With multiple choices available in the markets, we might be baffled that why going for Pakistani suits could be optimum solution. Even if you are shopper and confused over choices, do read the blog for the next. Exclusiveness: - The long style suits and class apart embroidery is perfect enough to captivate our attention in one glance. In the Pakistani suits you will find that even the volume of the salwar is little lower as compared to Patiala suits. Every pattern does exhibit the distinctiveness of fashion. The mesmerizing hues, shades and different hemlines are worth a grab. Heavy work done up: - Major focus here is to give the best and excellent craftsmanship. There is lot of trio of hand and machine work done on the Pakistani suits. These suits could be perfectly worn by the brides or one could even team them on in weddings or other occasions. When it comes to Pakistani suits the traditional sindhi work or zardosi work is renowned and famous one. The delicate stone work and beautiful settings on the dress will make your appearance distinctively classy. Durability and longevity: - when we buy ethnic pieces the foremost important thing we see is complete finish. The designer boutique does make dresses with good quality of fabric that lasts for longer period of time. Different sizes:- The best part of relying on the boutiques is that you don't need to make any compromises on the size part of it, the availability of different sizes does make it worth a buy.


text:
Aleve pain reliever sales advanced 27.5% to $302.3 mil. (E1=$1.33) in 2006 (ended Dec. 31), Bayer announces March 15. One-A-Day achieved sales growth of 5.1% to $165.1 mil. and Alka-Seltzer revenues increased 6.3% to $101 mil. for the year, firm adds. The brands helped drive sales of Bayer's Consumer Health Consumer Care Division, which jumped 7.5% to $3.37 bil. for the year, the company reports, noting it doubled sales of its OTC pharmaceuticals franchise during the year. The Consumer Health segment had net sales of $5.66 bil., representing growth of 8.1%. The company is continuing expansion of the Consumer Health division abroad, particularly in China, with the recent purchase of OTC company Topsun's cough/cold portfolio (1"The Tan Sheet" Oct. 30, 2006, p. 9). The HealthCare group's net sales grew 46.6% to $15.62 bil., and earnings before interest, taxes, depreciation and amortization before special items soared 75.7% to $3.48 bil. Bayer is targeting underlying EBITDA margin growth of about 27% in HealthCare in 2009...
Bayer Increases Chinese Presence With Topsun Cough/Cold Buy
Bayer expects its purchase of Topsun Science & Technology's nonprescription cough and cold portfolio to "substantially increase Bayer Consumer Care's presence in China, one of the fastest growing OTC markets in the world," the firm states Oct. 25
Health And Wellness Trademark Review 14 January, 2020
Trademarks are registered and published for opposition with the US Patent and Trademark Office and are published weekly in the agency's Official Gazette.
Claim That Supplement Boosts Children's Focus Could Spur FTC Attention
Creekside Natural Therapeutics might hear from the FTC after failing to show in an industry self-regulation forum that it would correct misleading claims for its Focused Mind Jr. supplement promoted as an alternative to ADHD drugs.
Subject: Bayer


text:
/* showip.c -- takes a hostname, returns an ip. */

/* -- Preamble -- */
#include<stdio.h>
#include<string.h>
#include<sys/types.h>
#include<sys/socket.h>
#include<netdb.h>
#include<arpa/inet.h>
#include<netinet/in.h>

/* --- Main --- */
int main (int argc, char *argv[]) {

  struct addrinfo hints, *res, *p;
  int status;
  char ipstr[INET6_ADDRSTRLEN];

  //incase too few/many args given, raise error
  if (argc != 2) {
    fprintf(stderr, "usage: showip hostname\n");
    return 1;
  }

  /* sin_zero (which is included to pad the structure to the length of a
  struct sockaddr) should be set to all zeros with the function memset()*/
  memset (&hints, 0, sizeof hints);

  hints.ai_family = AF_UNSPEC; // AF_INET or AF_INET6 to force version
  hints.ai_socktype = SOCK_STREAM;

  // case raise error
  if ((status = getaddrinfo(argv[1], NULL, &hints, &res)) != 0) {
    fprintf(stderr, "getaddrinfo: %s\n", gai_strerror(status));
    return 2;
  }

  //
  printf("IP Addresses for %s:\n\n", argv[1]);
  //for address in sockaddr struct, print address and version of protocol
  for (p = res; p != NULL; p = p->ai_next) {
    void *addr;
    char *ipver;
    // get the pointer to the address itself,
    // different fields in IPv4 and IPv6:

    //if IPv4
    if (p -> ai_family == AF_INET) {

      struct sockaddr_in *ipv4 = (struct sockaddr_in *) p -> ai_addr;
      addr = &(ipv4 -> sin_addr);
      ipver = "IPv4";
    }

    else {
      // IPv6
      struct sockaddr_in6 *ipv6 = (struct sockaddr_in6 *) p -> ai_addr;
      addr = &(ipv6 -> sin6_addr);
      ipver = "IPv6";
    }

    // convert IP to a string and print it.
    inet_ntop(p -> ai_family, addr, ipstr, sizeof ipstr);
    printf("[+] %s: %s\n", ipver, ipstr);
  }
  /* When all done with the linked list that getaddrinfo() allocated
     for us, we should free it up with a call to freeaddrinfo().*/
  freeaddrinfo(res);

  return 0;
}

redpajama_set_name: RedPajamaGithub


text:
→ Samuel Barber - more than just Adagio
Samuel Barber - more than just Adagio
Samuel Barber was born in Pennsylvania in 1910, and despite his family's best attempts for him to be an all-American football-playing boy, his musical talent was apparent from an early age – as was his distaste for football, he wrote his mother a letter apologising for wanting to be a composer and begging not to be sent to play it. Many of us can relate, if not to the compositional talent but for the longed-for sick note.
Much of his music is for the voice, perhaps because Barber was a talented baritone – at one time he considered making this his profession. Luckily for us though he chose composition, and by his twenties he was getting considerable fame and attention. His music is characterised by having long lyrical lines and use of instrumental colour. But more than anything, what makes it distinctive is the way his music wears its heart unashamedly on its sleeve – often being an expression of profound emotion, something that led to him rapidly gain popularity, even if, at times, his music was criticised for being 'old fashioned'.
Today Samuel Barber is mainly known for one piece; his Adagio for strings, made famous through use in the film Platoon. None of his many other compositions has quite attained the same level of fame, which is a shame as they are well worth discovering.
Knoxville, Summer of 1915 is a piece for voice and orchestra which he wrote in 1947, at the height of his fame. The piece is usually sung by soprano but its text is sung from the point of view of a male child. That text is by the writer James Agee, and when Barber first read it it provoked an immediate reaction, reminding him of his own childhood. Upon deciding to set it to music he completed the bulk of the piece in just ninety minutes.
The music describes a warm summers evening in an American town, with, to be honest, nothing much happening, as is probably typical of small-town America. Knoxville contains many of Barber's hallmarks – long flowing melodies, lush orchestration and rich textures, and a certain wistfulness and nostalgia. There's also a somewhat dreamlike quality to it, with it sometimes being hard to identity the speaker, and them sometimes talking as an adult rather than a child. Barber talked of it expressing 'a child's feelings of loneliness, wonder and lack of identity in that marginal world between twilight and sleep'.
The piece ends with the singer talking of being put to bed and the music slowly drifting upwards, almost floating, evoking sleep and dreams.
Hear Barber's Knoxville performed by Royal Northern Sinfonia and Francesca Chiejina on Friday 28 May, 7.30pm.