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1d
comment If A is an infinite set, prove that |A| = |A\F| if F is finite
The important question here is : how do you define finite/infinite? In set theory, there are options.
1d
comment Algebric equation problems
Where did you find this problem? P.S. : Your last comment should be added in the question, not as a comment.
2d
answered Understanding the connection of the roots of an irreducible polynomial and a basis for field extensions
Aug
22
comment Action of ${\rm Aut}(G)$ on $G$
@sebastian : ahhh. Okay! Yeah you need to watch out about aaaall the words you write! It makes people ponder... ;)
Aug
22
comment Action of ${\rm Aut}(G)$ on $G$
@sebastian : I'm thinking about the converse and looking at your motivation ; how is it "clear" that $|G|=2$ in your question? I can see how it could be true but it does not seem obvious to me. Maybe I am missing something obvious.
Aug
22
comment Action of ${\rm Aut}(G)$ on $G$
@Alex M. : "Elementary abelian group" is a standard group theory term, just google it. It means that the exponent of $G$ is a prime number, or if you prefer, that every non-trivial element of $G$ has the same order (which then has to be prime by Lagrange's theorem).
Aug
21
answered Action of ${\rm Aut}(G)$ on $G$
Aug
17
comment 10 red cars, 10 blue cars, 10 green cars are distributed randomly in a line. What is the expected number of times a red car precedes a blue car?
My answer was marked "wrong" by the presumed downvoter, but to be fair "preceding a blue car" does not have to imply that you precede it immediately... I think it is pretty clear that my answers assumes that my definition of "preceding" just means that it arrives before in the line. For the other definition look at the other answers.
Aug
13
answered 10 red cars, 10 blue cars, 10 green cars are distributed randomly in a line. What is the expected number of times a red car precedes a blue car?
Aug
12
comment Ring of rational 2x2 matrices has no proper ideals
Right. But this should be added to the answer, it's not hard to understand but worth mentioning! I didn't think that the fact that the matrices were $2 \times 2$ would be relevant (you can't use your trace argument if we work with $n \times n$ matrices, but the result is also true for $n \times n$ matrices).
Aug
12
comment Ring of rational 2x2 matrices has no proper ideals
You assume the field is closed, while it doesn't have to be! The answer linked in the comments explains how to do it
Aug
12
comment Taking the limit $\lim_{p\rightarrow \infty} \left( \frac{\|f\|_\infty}{\|f\|_p}\right)^p$
@user229922 : You mean $(1+1/n)^n$? ;)
Aug
11
comment if $ L = \lim_{x\to1^-} \sum_{n=1}^\infty a_nx^n$ then $\sum_{n=1}^\infty a_n = L$
@ajotatxe : Do you see it in the assumptions? :P
Aug
8
comment Limit using Poisson distribution
@BCLC : Yes, because the normal distribution is given by a smooth (and in particular continuous) density.
Aug
8
comment Limit using Poisson distribution
@BCLC : That's precisely the CLT : that a sum of i.i.d variables (minus the average divided by standard deviation) converges in distribution to the normal distribution, that is, $\lim_{n \to \infty} \mathbb P \left( \frac {Y_1 + \cdots + Y_n - \mu}{\sigma} \le x \right) \to \mathbb P \left(Z \le x \right)$ when $Y_i$ follows some distribution of mean $\mu$ and variance $\sigma^2$ and $Z \sim \mathcal N(0,1)$. So I did not really switch $\lim$ and $\mathbb P$ properly speaking, I just applied the CLT ; that's because the CLT only guarantees convergence in distribution.
Aug
4
revised Finding the cardinality of $\{ X \subseteq \mathcal{P}(A) : |X| \leqslant 1 \}$.
deleted 1 character in body
Jul
27
revised Is there a unique homomorphism of $\mathbf Z $ into $A$?
english error
Jul
27
comment What would be interesting maps to use on that Eudoxus reals?
I think the interesting question is rather : how do you even represent a rational number using this notion of almost homomorphism? It doesn't seem trivial to guess.
Jul
24
comment Prove that there are infinitely many composite numbers of the form $2^{2^n}+3$.
@user95864 : Yes, that's it!
Jul
23
revised Prove that there are infinitely many composite numbers of the form $2^{2^n}+3$.
added 21 characters in body