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Jul
23
comment Proving that if $p^2 = a^2 + 2b^2$ then also $p$ can be written in form $a^2 +2b^2$
With hindsight splitting into the three cases was unnecessary, you only need that $(p)$ splits into one or two prime ideals, but maybe it's instructional to leave it in.
Jul
11
comment For what functions is this theorem correct?
@joriki The cardinality. One of the conditions for the theorem to be true is surely that preimages are finite.
Jul
11
comment For what functions is this theorem correct?
@joriki Apologies, I meant preimage of an element in the image. I thought you were being sarcastic.
Jul
11
comment For what functions is this theorem correct?
@joriki How is that relevant?
Jul
9
comment For what functions is this theorem correct?
That is correct.
Jun
23
comment Prove that for $\alpha$ an ordinal, $\alpha \le \omega^\alpha$.
Aha, thanks. I see.
Jun
23
comment Prove that for $\alpha$ an ordinal, $\alpha \le \omega^\alpha$.
My non-understanding lies elsewhere: why does the result follow from this?
Mar
23
comment Dirac delta implies continuous?
@Woodface I don't have a rigorous one.
Mar
20
comment Show that there are only finitely many subgroups of $F$ in which $H$ can be of finite index.
$F$ is free on how many generators?
Mar
20
comment Simple proof verification
What does $\Gamma_i$ mean?
Mar
15
comment Badly behaved, but easy-to-manipulate examples of rings to test hypotheses on
@N.H. Oh, thanks! Maybe you could answer with an example if you have the time?
Mar
12
comment 'Elementary' proof of $\tilde{X}$ is contractible iff $\pi_n(X) =0 \forall n \ge 2$.
Sorry, why does it follow that $\pi_1(X)= \pi_1(\tilde{X})$ for $n \ge 2$?
Mar
10
comment If $S_\epsilon$ is dense for all $\epsilon$, is $S_0$ dense?
The italics are directed not at anyone who has already answered, but at potential answerers.
Mar
9
comment Discriminant is the unique invariant of $\text{SL}_2\mathbb{Z}$ acting on polynomials.
Leox, this answer is actively detrimental to my attempts to understand this, in that having an answer reduces answerer-traffic, and this answer is basically a rephrasing of the question with the addition of 'some theorem proves it'. Please either delete this or at least provide a link to the proof of that result (I can't find a proof by googling). Thank you.
Mar
9
comment If $S_\epsilon$ is dense for all $\epsilon$, is $S_0$ dense?
Baire, measures or whatever are fine to use, this isn't a homework, but I doubt they will be that useful here, even if it feels a little Bairey.
Mar
7
comment Is the pushforward measure a categorical-theoretic pushout?
@tomasz I just guessed about it being a pushout, what I really wanted to know was whether it is universal in some category. Could you consider fleshing out your description of how pushforward maps are universal into an answer?
Feb
13
comment 'Elementary' proof of $\tilde{X}$ is contractible iff $\pi_n(X) =0 \forall n \ge 2$.
@KevinCarlson Thank you, I will edit.
Feb
13
comment 'Elementary' proof of $\tilde{X}$ is contractible iff $\pi_n(X) =0 \forall n \ge 2$.
@NajibIdrissi Yes.
Jan
28
comment Conservation of bilinear forms and conjugation
@OlivierBégassat Could you clarify what the matrix of a bilinear form is?
Jan
27
comment Conservation of bilinear forms and conjugation
@OlivierBégassat Yes.