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age 25
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Aug
20
asked Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
Aug
20
comment Surprising Generalizations
@Qiaochu: Do you have a reference where I could see the details of this example? Thank you.
Aug
12
accepted Are the axioms for abelian group theory independent?
Aug
10
comment Abelian categories and axiom (AB5)
Did you check in chapter 3 of Mitchell's "Theory of Categories"? If I remember correctly, Mitchell uses the terminology $C_3$ instead of $AB_5$.
Aug
10
comment Existence of an embedding from the rational numbers to $(0,1)$
Aha! I seemed to recall reading about this interesting thereom a couple of years ago. Of course, it was in Henno Brandma's collection of notes on topology. This one in particular is at.yorku.ca/p/a/c/a/25.htm .
Aug
7
awarded  Nice Question
Aug
6
comment Are the axioms for abelian group theory independent?
Thanks, this is a very nice example too, especially taking into account Asaf's comment. @Qiaochu: care to elaborate?
Aug
6
comment Are the axioms for abelian group theory independent?
Fantastically simple, thanks! Makes me feel a little dumb though for not finding an example after playing around so much :)
Aug
6
asked Are the axioms for abelian group theory independent?
Aug
6
awarded  Good Question
Aug
4
comment What's the “geometry” in “geometric multiplicity”?
Well, an eigenspace is a vector subspace, so if the geometric multiplicity is 1 then it is a line through the origin, if it is 2 then it is a plane through the origin, etc. This is just a wild guess, but it seems plausible that the name might come from this interpretation.
Aug
3
comment Euler's Constant: The asymptotic behavior of $\left(\sum\limits_{j=1}^{N} \frac{1}{j}\right) - \log(N)$
@DJC: I think it is a bit shocking to use displaystyle in the title.
Aug
3
revised Normal closure of a radical extension is radical
edited for clarification on what is asked
Aug
3
comment Normal closure of a radical extension is radical
I must say I'm a bit surprised by the lack of answers to this question. It shouldn't take too long to answer for somebody comfortable with Galois theory.
Aug
1
revised Normal closure of a radical extension is radical
edited tags
Jul
31
comment Normal closure of a radical extension is radical
@Dylan: What puzzles me is that if all the details I wrote out are necessary, then I think the author should have been a bit more verbose on the proof...
Jul
31
asked Normal closure of a radical extension is radical
Jul
28
comment Bernoulli's representation of Euler's number, i.e $e=\lim \limits_{x\to \infty} \left(1+\frac{1}{x}\right)^x $
Related: planetmath.org/?op=getobj&from=objects&id=10170
Jul
27
comment What does “formal” mean?
It should be noted that the first sense includes a really vast spectrum of degrees of formality. The way I see it, it includes usual textbook proofs (e.g. Folland's proof of Radon-Nikodým theorem is 'formal'), and 'logically' formal proofs, as in en.wikipedia.org/wiki/Formal_proof , which also serves as input for automated proof checking.
Jul
26
comment For what functions does $\int_{-\infty}^{\infty}x \sin(f(x))\,dx$ converge?
If the function is differentiable, "grows fast enough" seems to imply some condition on $\lim_{x\to \infty} f'(x)$.