## Search found 42 matches

- Fri Aug 21, 2009 8:48 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0626: "Newton and Leibniz"
- Replies:
**213** - Views:
**58076**

### Re: "Newton and Leibniz" Discussion

I can already see what the commenters at XKCD sucks are going to say about this. "What? Me no get the joke" FIRST-YEAR CALCULUS IS EASY. GET OVER YOURSELF. So it's not a reference to graduate school math. Who cares? Um, if you had read for context, you would have seen that my point was di...

- Fri Aug 21, 2009 6:07 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0626: "Newton and Leibniz"
- Replies:
**213** - Views:
**58076**

### Re: "Newton and Leibniz" Discussion

And what's even better is all the people not catching the CSI: Miami reference. I thought that was a meme of the internet by now. Oh, hooray. The internet meme is one-liners with sunglasses. So the joke is Newton making a lame one-liner pun with sunglasses. HOORAY. Also the webcomic of romance, sar...

- Fri Aug 21, 2009 4:10 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0626: "Newton and Leibniz"
- Replies:
**213** - Views:
**58076**

### Re: "Newton and Leibniz" Discussion

Looks like neoliminal is keeping his dignity.

Also, sweet jesus in heaven. Xkcd "humor" is now bordering on Brightly Wound. RANDALL, GO ON SABBATICAL. GIVE YOURSELF TIME TO GET IDEAS. IF GARY LARSON NEEDED IT, YOU SURE AS HELL AREN'T ABOVE IT.

Also, sweet jesus in heaven. Xkcd "humor" is now bordering on Brightly Wound. RANDALL, GO ON SABBATICAL. GIVE YOURSELF TIME TO GET IDEAS. IF GARY LARSON NEEDED IT, YOU SURE AS HELL AREN'T ABOVE IT.

- Wed Aug 19, 2009 3:40 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0625: "Collections"
- Replies:
**137** - Views:
**34309**

### Re: "Collections" Discussion

Have to agree with SirMustapha and Ithaca. This comic is almost as bad as "Haiku Proof". And, as has been increasingly the case, discussion just turns into a pissing contest to see who wins at the topic in the comic. (In this case, who has the most Pratchett books.) Then again, it's not as...

- Fri Aug 14, 2009 3:59 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0622: "Haiku Proof"
- Replies:
**126** - Views:
**41930**

### Re: "Haiku Proof" discussion

This comic is painful. Last two weeks have been pretty bad, but this one is particularly awful. It is also a bit sad that the "webcomic of romance, sarcasm, math and language" has so little math. In fact, the whole "xkcd is great at science" hype has been looking pretty silly for...

- Thu Jul 30, 2009 3:41 pm UTC
- Forum: Mathematics
- Topic: Continously adding digits to a number
- Replies:
**15** - Views:
**1572**

### Re: Continously adding digits to a number

notzeb wrote:um... after you stick a 3 onto the end of the number, it isn't of the form 2a5b. "Problem" solved.

Oooh... color me silly.

- Thu Jul 30, 2009 7:22 am UTC
- Forum: Mathematics
- Topic: Continously adding digits to a number
- Replies:
**15** - Views:
**1572**

### Re: Continously adding digits to a number

It remains to prove that there exists r such that (3n+1)10 r −1 isn't a power of three. (Nice use of the big guns, by the way.) The answer to this specific problem can be got by subtracting consecutive terms: [(3n+1)10 r+1 −1] - [(3n+1)10 r −1] = 9(3n+1)10 r So 9 is the biggest power of 3 dividing ...

- Thu Jul 30, 2009 7:13 am UTC
- Forum: Mathematics
- Topic: Continously adding digits to a number
- Replies:
**15** - Views:
**1572**

### Re: Continously adding digits to a number

Good starting observations, and nice proof for n not of the form 2 a 5 b . Unfortunately I couldn't come up with a fix, and ended up with a proof for the general case instead. Here it is: let p be a prime factor of the number 10n+3. Obviously it can't be 2 nor 5. Now put k=p. By Fermat's Little, we ...

- Sun Jul 26, 2009 5:20 pm UTC
- Forum: Mathematics
- Topic: Book Club: Mathematics: Its Contents... discussion
- Replies:
**50** - Views:
**5312**

### Re: Book Club: Mathematics: It's Contents... discussion

Perhaps I'm taking things more slowly than most, since right now I'm a bit swamped with work (thesis writing), but I was somewhat taken aback by the fact that discussion jumped straight into chapter 2, "Analysis". I just finished reading chapter 1, and it sure is interesting! Did you guys ...

- Sat Jul 25, 2009 11:02 pm UTC
- Forum: Mathematics
- Topic: Favorite math jokes
- Replies:
**1452** - Views:
**485803**

### Re: Favorite math jokes

Oh, the thread is too long, I'll just post this joke and hope it isn't a repeat! The sad thing is, if people would read the thread, there wouldn't be a dozen copies and fifty slight variants of each single joke posted. Then the thread would still probably be under 10 pages long, and it would be qui...

- Thu Jul 23, 2009 7:14 pm UTC
- Forum: Mathematics
- Topic: Area of the Primes / Overstimulated
- Replies:
**6** - Views:
**954**

### Re: Area of the Primes / Overstimulated

I haven't checked your MatLab code (I don't really know MatLab), but it is to be expected that the sum increases very slowly. In fact, if p n denotes the n-th prime, it is a theorem that \sum_{i=1}^n \frac{1}{p_i} \ \approx \ \log \log n So it's quite reasonable that, at 50,000, you should see somet...

- Sat Jul 18, 2009 6:06 am UTC
- Forum: Mathematics
- Topic: Graph Theory (Bollobás) Discussion
- Replies:
**21** - Views:
**2302**

### Re: Graph Theory (Bollobás) Discussion

RabidAltruism, I don't mean to be a spoilsport, but perhaps that wasn't the best possible acquisition. First, it's not really by Bollobas, but a collection of survey papers by many authors, edited by Bollobas. Not necessarily a bad thing, but I'm not familiar with any of the other authors' styles, e...

- Fri Jul 17, 2009 12:19 pm UTC
- Forum: Mathematics
- Topic: Graph Theory (Bollobás) Discussion
- Replies:
**21** - Views:
**2302**

### Re: Graph Theory (Bollobás) Discussion

Let me just add a word of encouragement: I've worked through about half that book, and it is an EXCELLENT book. The prose is clear and enlightening, the proofs elegant, and the overall structure very wel thought-out. If anyone else has a fancy for combinatorics, I can recommend pretty much everythin...

- Fri Jul 17, 2009 12:16 pm UTC
- Forum: Mathematics
- Topic: A Happy Prime Problem
- Replies:
**11** - Views:
**1867**

### Re: A Happy Prime Problem

I have no insight into the original problem, but here's a fun one (which I have not been able to solve either). All our integers will be expressed in base 10 (this is arbitrary). Consider the happy function, given by the sum of the squares of the digits: happy(21) = 2²+1¹ = 5 happy(123) = 1²+2²+3² =...

- Fri Jul 17, 2009 11:48 am UTC
- Forum: Mathematics
- Topic: Mathematics: Discovered or Invented?
- Replies:
**39** - Views:
**4740**

### Re: Mathematics: Discovered or Invented?

we didnt set up the rules. [...] we didnt determine that if you take two neutrons, there is twice as many as if we take one. Yes, we did set up those rules, when we (our brains) elected to interpret a section of sensory input as "one neutron", as something separate from everything else. Y...

- Fri Jul 17, 2009 9:09 am UTC
- Forum: Mathematics
- Topic: Mathematics: Discovered or Invented?
- Replies:
**39** - Views:
**4740**

### Re: Mathematics: Discovered or Invented?

I'm going to say some things which have been beaten to death in the philosophy of math. We invented pi for the very simple reason that we invented circles. There are no circles in the real world. We also invented the notion of discreteness which allows us to count things. It is your mind that separa...

- Fri Jul 17, 2009 8:59 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

I very much do want to invite comparison of the "validity" of a proof to other properties by which we judge it. What makes validity (as we interpret that word today) so special? What do we even mean by validity? We seem to be talking at cross-purposes. I'm using "validity" of a ...

- Thu Jul 16, 2009 11:12 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

I think antonfire was talking about preferences for different kinds of valid proofs, not preferring invalid proofs. That doesn't follow at all from what he was saying. I don't think antonfire advocates invalid proofs. Antonfire is probably every bit as able at mathematics as I am, or more. Neverthe...

- Thu Jul 16, 2009 10:42 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

To get back on topic, I just wanted to make clear my original point. I first said that "formal systems are not the holy grail", and t0rajir0u said something that could be read as, "yeah, everyone does math their own way, and formal systems are as good as anything else". (I don't ...

- Thu Jul 16, 2009 10:36 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

Standards for the loosest acceptable proof for a*0=0 vary from "it's obvious" to the full axiomatic proof with justifications for each step. I'm not sure if you meant to pick any example and went with "0=0" by accident, but it's not a good one. In fact, "0=0" i...

- Thu Jul 16, 2009 7:08 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

Hear, hear. The community standards for what constitutes an acceptable proof are just that; standards. They vary over time like any other set of standards. I sympathize with one possible reading of your post, but maybe there's room for misunderstanding. I don't think you misunderstand anything, jud...

- Thu Jul 16, 2009 6:34 am UTC
- Forum: Mathematics
- Topic: Mathematics: Discovered or Invented?
- Replies:
**39** - Views:
**4740**

### Re: Mathematics: Discovered or Invented?

For many interested laypeople who are not practising mathematicians, mathematics has a sort of mystical aura of awesomeness about it. Things are "deep", "eternal" and whatnot. Though there's nothing necessarily wrong with that, it can negatively affect one's clear thinking about ...

- Sat Jul 11, 2009 9:36 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

Continuing with point (1) and the objection that Euclid does not state nor prove the comparability of any pair of natural numbers. One thing the objector claimed was that this was dealt with by the advent of "rigor" a hundred years ago, where people started writing down explicit axiom syst...

- Sat Jul 11, 2009 7:58 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

t0rajir0u and skeptical scientist: I'm glad you found my post to be of interest. I agree with both your statements on point (1), and they are important things to keep in mind. Nevertheless, I would like to address more directly the question "do mathematical logic and formal systems provide a gr...

- Sat Jul 11, 2009 7:48 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Re: Some points on mathematical logic and "rigor"

Let's tackle point (1). I'll start by reviewing a paradigmatic argument about the "lack of rigor" of earlier mathematicians, presented by forum member Gaydar2000SE's. It is well-known that Euclid's Elements contains a proof that there are an infinite number of primes. Gaydar2000SE contends...

- Sat Jul 11, 2009 7:12 am UTC
- Forum: Mathematics
- Topic: Some points on mathematical logic and "rigor"
- Replies:
**27** - Views:
**4299**

### Some points on mathematical logic and "rigor"

Dear forum, quite recently, there were a couple of threads on "rigor" in mathematics, and the inevitable accompanying discussion of mathematical logic and its perceived achievements. At least one forum member felt that "rigor" is a newcomer to mathematics, originating only "...

- Sat Jul 11, 2009 5:03 am UTC
- Forum: Mathematics
- Topic: Egyptian fractions
- Replies:
**13** - Views:
**2543**

### Re: Egyptian fractions

Open? It was proved in 2003 - http://arxiv.org/PS_cache/math/pdf/0311/0311421v1.pdf. Oh my, so it was. I guess I should have read the Wikipedia page. It's a rather ingenious argument, by the way. The only non-elementary bit of mathematics that goes into the result seems to be the prime number theor...

- Fri Jul 10, 2009 10:53 am UTC
- Forum: Mathematics
- Topic: Egyptian fractions
- Replies:
**13** - Views:
**2543**

### Re: Egyptian fractions

PM 2Ring, it's true, egyptian fractions give rise to some pretty interesting problems, with a decidedly unique taste. Here are a couple: [Fun exercise.] Let q be a rational number between 0 and 1. We call 1/x + 1/y + ... + 1/w a strict egyptian representation of q if x,y,...,w are distinct positive ...

- Thu Jul 09, 2009 10:31 am UTC
- Forum: Serious Business
- Topic: Life: Overrated Coincidence or Spiritual Goal?
- Replies:
**70** - Views:
**6292**

### Re: Life: Overrated Coincidence or Spiritual Goal?

The greatest goal of the human species is to truly know the meaning of everything. Why they are here, how they works, the meaning of life, etc... I'm sorry, when did the human species last vote on its greatest goal? Was it unanimous? Do they have a new vote every time someone is born? And seriously...

- Thu Jul 09, 2009 7:55 am UTC
- Forum: Mathematics
- Topic: Egyptian fractions
- Replies:
**13** - Views:
**2543**

### Re: Egyptian fractions

You can also add any perfect square simply because all of the numbers can be the same. ie, 6+6+6+6+6+6=36 1/6+1/6+1/6+1/6+1/6+1/6=1 You're quite right, but it was the first thing we noticed on this thread! :o) You're also right regarding your egyptian/strictly egyptian question. Indeed, it seems (n...

- Tue Jul 07, 2009 10:17 am UTC
- Forum: Mathematics
- Topic: Egyptian fractions
- Replies:
**13** - Views:
**2543**

### Re: Egyptian fractions

A small observation I just made, which answers the last question: lemmas 1 & 2 can never be used to show that any prime number works. (Look at the conclusions in them.) Nevertheless, some prime numbers work! The smallest of these is 11: 2 + 3 + 6 = 11 1/2 + 1/3 + 1/6 = 1 The plot thickens... Her...

- Tue Jul 07, 2009 9:48 am UTC
- Forum: Mathematics
- Topic: Egyptian fractions
- Replies:
**13** - Views:
**2543**

### Re: Egyptian fractions

This problem is fascinating! I haven't solved it, but here's some partial progress. We'll say that a natural number N works iff there are natural numbers x 1 ,...,x i such that x 1 +...+x i =N and 1/x 1 +...+1/x i =1. The first obvious thing I noticed was that perfect squares always work. You just t...

- Sun Jun 21, 2009 10:27 am UTC
- Forum: Mathematics
- Topic: Greater achievement - Perelman's or Wile's proof?
- Replies:
**23** - Views:
**3411**

### Re: Greater achievement - Perelman's or Wile's proof?

I mean, what if Wiles first proved that elliptic curve thing, forgot how it was called. And then some other person came with 'Yeah, but if fermat's is true, then some elliptic curves aren't modular, didn't some guy 50 years back prove that ALL elliptic curves are?', would they then posthumously awa...

- Fri Jun 19, 2009 8:34 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0599: "Apocalypse"
- Replies:
**158** - Views:
**56249**

### Re: "Apocalypse" Discussion

Daniel Kleitman, a combinatorialist at MIT (not a consultant), is famous for having solved more than a handful of problems proposed by Erdos(*), and in the process acquired an Erdos number 1. He also consulted for "Good Will Hunting", which gave him a Bacon number 2 via Minnie Driver. http...

- Wed Apr 02, 2008 7:51 am UTC
- Forum: Mathematics
- Topic: Levels of Infinity (theory)
- Replies:
**63** - Views:
**7306**

### Re: Levels of Infinity (theory)

The standard real numbers are complete, and do not have infinitesimals. I think the term you had in mind was "archimedean" rather than "complete". There is a rather simple proof that something very "like" the real numbers, but with infinitesimals, exists. To wit, let T...

- Tue Feb 19, 2008 11:17 pm UTC
- Forum: Mathematics
- Topic: Pure Maths - putting it all together
- Replies:
**33** - Views:
**3515**

### Re: Pure Maths - putting it all together

Yakk wrote: Neat -- are those equivalencies more interesting than "they are equally true"? Yes; the point is that the equivalence is "much easier" to prove than the theorems themselves, in the sense that very weak logical systems can do it. In particular, logical systems which c...

- Tue Feb 19, 2008 5:22 pm UTC
- Forum: Mathematics
- Topic: Realism?
- Replies:
**18** - Views:
**1903**

### Re: Realism?

dosboot wrote: It seems to bring into question whether model theory is actually relevant to mathematics. Stepping outside an arbitrary set theory and studying it with model theory seems as relevant as stepping outside model theory and studying it with an arbitrary set theory. Oh yes, model theory i...

- Mon Feb 18, 2008 11:20 pm UTC
- Forum: Mathematics
- Topic: Pure Maths - putting it all together
- Replies:
**33** - Views:
**3515**

### Re: Pure Maths - putting it all together

Robin S wrote: That is why all I am looking for is an outline of how to build up from ZFC to other areas of maths, rather than a way of doing advanced maths in set-theoretic notation. You've said this a couple of times already, in response to people showing how to define standard mathematical struc...

- Mon Feb 18, 2008 9:01 am UTC
- Forum: Mathematics
- Topic: Realism?
- Replies:
**18** - Views:
**1903**

### Re: Realism?

ErrantBit writes: How do higher-order logics permit theories with no countable model? This isn't so hard to see. How does first-order logic allow for theories without a finite model? Choose a language with at least one function symbol, f, and equality, =, and consider the following theory (in forma...

- Mon Feb 18, 2008 8:22 am UTC
- Forum: Mathematics
- Topic: Pure Maths - putting it all together
- Replies:
**33** - Views:
**3515**

### Re: Pure Maths - putting it all together

Kolmogorov & Fomin is an excellent book, particularly because, when a concept is introduced, they give examples which are interesting in their own right; many of which actually motivated the development of the abstract theory. (Don't you hate it when textbooks give the trivial example first? &qu...