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olivier dot begassat dot cours at gmail dot com


Dec
10
comment Latin phrase for “accepting without proof”
@DennisGulko look at the poster's reputation, it takes 50 reputation to post comments.
Dec
10
answered Prove or disprove a function is continuous
Dec
10
comment Numbers permutation
+1 nice answer, and I never knew of that result you link to.
Dec
9
comment Question about proof of subgroups
@YoavFridman Could edit your question to contain the exact statement that you are to prove? One possible correct statement would be $$\Big(\forall a\in G, aH=Ha\Big)\quad\Longleftrightarrow\quad\Big(\forall a\in G\forall h\in H, a^{-1}ha\in H\Big)\,.$$
Dec
9
comment Question about proof of subgroups
As it stands, the statement is incorrect, or at least very ambiguous. Are $a$ and $h$ fixed at the beginning, or are you trying to prove, given $a\in G$ that $$aH=Ha\quad\Longleftrightarrow\quad\Big(\forall h\in H,a^{-1}ha\in H\Big)$$?
Dec
8
comment How to prove or disprove that $\gcd(ab, c) = \gcd(a, b) \times \gcd(b, c)$?
Have you tried numerical examples? You should do so to either get a counter example, or on the contrary, convince yourself that the statement might be true.
Dec
8
comment What is the single most influential book every mathematician should read?
I liked the book (and thus upvoted). It's been years since I read it, but I remember working out some calculations with a recursive function $G$ that I thought were very cool back then.
Dec
7
answered Conjugation of $3$-cycles in $A_5$
Dec
7
answered Symmetrical endomorphisms and quadratic forms
Dec
7
revised Does $\varphi_1(K) \cong \varphi_2(K)$ imply $H\rtimes_{\varphi_{1}} K \cong H\rtimes_{\varphi_{2}} K$?
added 576 characters in body
Dec
5
comment The intuition behind generalized eigenvectors
@AsafKaragila Well, then it's only fitting a three year old comment should receive a reply today!
Dec
5
comment The intuition behind generalized eigenvectors
@AsafKaragila Oh ... sorry about that : ) this question must have received a new answer, or have been bumped up by the site for it landed on my front page! I never noticed this was so old ^^
Dec
5
comment The intuition behind generalized eigenvectors
@AsafKaragila This notation is relatively common in functional analysis books, together with $\mathrm{R}(T)=\mathrm{Im}(T)$ for the range of $T$.
Dec
5
comment Is there a finite commutative semigroup $S$ with $S^2 = S$ which is not a monoid?
There are monoids with all elements idempotent. For instance take the product monoid $\lbrace +,0,-\rbrace^n$ where $0$ is the identity and $+\cdot -=+$ and $-\cdot +=-$. You can then remove the identity and get a finite semigroup $S$ with $S^2=S$.
Dec
4
comment Finite abelian group of order $a*b$
Or you could use a Bezout relation $ua+vb=1$ to produce an isomorphism $G\to G(a)\times G(b)$ by sending $g$ to the pair $(g^{vb},g^{ua})$.
Dec
3
comment Dot product and orthogonality?
Do you mean $\pm\pi/2$?
Dec
3
comment Homotopic maps to $S^n$
It would. One would probably have to argue that there are regular values that aren't attained on the border to make sure the argument goes through smoothly though, but that's easy.
Dec
3
comment Homotopic maps to $S^n$
I think it might follow from a local degree calculation : the degree is equal to the sum of $+1$s and $-1$s indexed by the inverse image of a regular value, where the sign corresponds to wether the map conserves or reverses orientation at that value. When glueing the two copies of $M$ together, you reverse orientation of one of them, and so the sum that calculates $deg(f\circ\pi)$ (which can be evaluated at a regular value of $f$) should be $\mathbf{Something}-\mathbf{Something}=0$.
Nov
29
comment Question on Rudin sequences?
Lovely! 15 characters
Nov
28
comment Relation between exponential map and parallel transport
Your proof attempts.