Doesn't this depend on all proofs being of finite length?

It's been a while since I did any of this kind of stuff, so I might just be missing something obvious

## Search found 15 matches

- Wed Aug 27, 2008 1:25 pm UTC
- Forum: Mathematics
- Topic: Godel and Geometry
- Replies:
**12** - Views:
**1784**

- Wed Aug 27, 2008 1:21 pm UTC
- Forum: Science
- Topic: The Most Sciencey-Sounding Word/Phrase You've Heard
- Replies:
**176** - Views:
**34652**

### Re: The Most Sciencey-Sounding Word/Phrase You've Heard

Someone's already mentioned Tegmark's "the mathematical universe" but that is chock full of crazy sounding phrases. Some other quality science phrases: “biological species” may be paraphyletic assemblages of populations united only by a plesiomorphy. Using synapomorphy as evidence of monop...

- Wed Aug 27, 2008 12:55 pm UTC
- Forum: Mathematics
- Topic: Something I just Noticed
- Replies:
**15** - Views:
**2115**

### Re: Something I just Noticed

And all prime numbers are one greater or one less than a multiple of four. That's hardly dependent on primes. Every odd number has the same property. That property is merely a set-up to split primes into two classes, one of which can be written as the sum of two integer squares and the others that ...

- Wed Aug 27, 2008 12:51 pm UTC
- Forum: Mathematics
- Topic: Godel and Geometry
- Replies:
**12** - Views:
**1784**

### Re: Godel and Geometry

Alfred Tarski formulated an alternative first-order theory of Euclidean geometry. According to the Wikipedia entry, Tarski and Steven Givant have proven that elementary geometry is both consistent and complete. Like the first-order Peano axioms for arithmetic, Tarski's system contains an infinite a...

- Mon Aug 25, 2008 4:24 pm UTC
- Forum: Mathematics
- Topic: More about xkcd number and other big numbers
- Replies:
**92** - Views:
**17757**

### Re: More about xkcd number and other big numbers

We could have a similar game trying to specify the largest infinite set in as few symbols as possible...

- Mon Aug 25, 2008 4:06 pm UTC
- Forum: Mathematics
- Topic: Something I just Noticed
- Replies:
**15** - Views:
**2115**

### Re: Something I just Noticed

And all prime numbers are one greater or one less than a multiple of four. All those one greater than a multiple of 4 can be written as the sum of two integer squares. None of the other class can. [edit] I should point out I didn't work this out: Pierre Fermat did. I just read about it in A Mathemat...

- Mon Aug 25, 2008 4:03 pm UTC
- Forum: Mathematics
- Topic: What's the genus of this surface?
- Replies:
**6** - Views:
**1374**

### Re: What's the genus of this surface?

I have a similar question. Imagine a sphere, and imagine axes coming out of its centre. Now drill through the sphere along each axis. The genus of the resulting shape, I think, is 5. But that seems a little weird. Am I making a mistake?

- Mon Aug 25, 2008 3:59 pm UTC
- Forum: Mathematics
- Topic: Iteration notation
- Replies:
**13** - Views:
**2673**

### Re: Iteration notation

You might want to pick another letter, since there's already something called lambda-calculus...

- Mon Aug 25, 2008 3:57 pm UTC
- Forum: Mathematics
- Topic: What augments well with pure math?
- Replies:
**13** - Views:
**2138**

### Re: What augments well with pure math?

Philosophy of Maths gets my vote. Or a high level formal logic course. I did a course which basically went through Godel's incompleteness theorems, but with massive detours into computability (halting problem etc) and model theory. It was great.

- Sun Aug 24, 2008 12:23 pm UTC
- Forum: Serious Business
- Topic: Philosophy in Education
- Replies:
**119** - Views:
**11678**

### Re: Philosophy in Education

and don't have any time for the likes of any of the Strawsons it's funny you should mention the strawsons; I saw Strawson the younger (Galen) speak a few months ago and it was the maddest talk ever. Most of the department were actually trying not to laugh. The talk was supposed to be about the phil...

- Sun Aug 24, 2008 12:14 pm UTC
- Forum: Mathematics
- Topic: How to: Graph Theory in Latex?
- Replies:
**8** - Views:
**5423**

### Re: How to: Graph Theory in Latex?

Like I said, I haven't used it myself, but I've seen some neat diagrams on category theory which were drawn with it. Graph theory pictures will presumably be fairly similar. I have had someone attempt to explain how to use it to me, and it did seem complicated...

- Sat Aug 23, 2008 8:18 pm UTC
- Forum: Logic Puzzles
- Topic: 2 + 2 = 5
- Replies:
**175** - Views:
**55582**

### Re: 2 + 2 = 5

division by 2π

from which we can conclude that [imath]2 \pi = 0[/imath]

- Sat Aug 23, 2008 8:07 pm UTC
- Forum: Serious Business
- Topic: Philosophy in Education
- Replies:
**119** - Views:
**11678**

### Re: Philosophy in Education

It's disappointing to hear people say things like "A lot of philosophy is nonsense" or "Most philosophy is wankery" etc. Without suggesting which bits of philosophy you think are worthless, comments like that just look ignorant. I personally think a lot of modern metaphysics and ...

- Sat Aug 23, 2008 7:41 pm UTC
- Forum: Books
- Topic: "Surely you're joking, Mr. Feynman!"
- Replies:
**27** - Views:
**7962**

### Re: "Surely you're joking, Mr. Feynman!"

James Gleick's biography of Feynman is called "Genius" and it's well worth reading.

- Sat Aug 23, 2008 7:31 pm UTC
- Forum: Mathematics
- Topic: How to: Graph Theory in Latex?
- Replies:
**8** - Views:
**5423**

### Re: How to: Graph Theory in Latex?

the xy-pic package might be useful to you.

I haven't used it myself and I don't know exactly how complex your demands are, but I've heard good things about this and specifically about the \xymatrix thing...

I haven't used it myself and I don't know exactly how complex your demands are, but I've heard good things about this and specifically about the \xymatrix thing...