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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 $\lim_{x\to \infty} f'(x)$.
Jul
26
awarded  Nice Question
Jul
20
comment Reference request: is mathematics discovered or created?
FWIW, I ended up writing the essay on something else (also math-related, though); so for those who were reluctant to throw out some ideas, be at ease: the answers and comments "only" contributed to my knowledge of these profoundly interesting matters.
Jul
19
comment Interpretation of a formula and truth
@Kaveh: thank you for your comments, I think I understand this better now.
Jul
18
comment Interpretation of a formula and truth
I understand. Still, I'm not fully convinced of why this is meaningful.