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bio website xavierm02.net
location France
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visits member for 3 years, 7 months
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Nov
22
comment When does this complex series converge?
For some $x$ expressed in terms of $z$, you series is $\sum\cfrac{x^n}{n}$ for which you should be able to answer the question.
Nov
18
comment Are simple extensions of isomorphic fields isomorphic?
Wouldn't $u\not=v=k$ give a trivial counterexample?
Nov
12
comment Intersection of Elements from Sets of Sets
Yes. Except that the notation $\|\cdot\|$ usually is for norms. I think $|x|$ is more common to denote the cardinal of $x$.
Nov
11
comment A field between $\mathbb{Q}$ and $\mathbb{R}$ ?
Well your field contains all rational numbers because you can take $y=0$.
Nov
11
comment Cardinality problem with multiple sets
The base case it trivial. What is given is to be used as a part of the induction step.
Nov
11
comment What permutations of matrix entries do row and column transpositions generate?
An interesting consequence of your statement is that row permutations and column permutations commute.
Nov
11
comment What permutations of matrix entries do row and column transpositions generate?
You can't get from $\begin{pmatrix} 1 & 1\\ 0 & 0 \end{pmatrix}$ to $\begin{pmatrix} 1 & 0\\ 1 & 0 \end{pmatrix}$
Nov
11
comment What permutations of matrix entries do row and column transpositions generate?
No. Being (or not) in the same row (or column) is preserved.
Nov
11
comment Zeroes of polynomials with several variables
It's false. Take $P\equiv 0$. For $P\not\equiv 0$ I think it's true though. To prove it, you should try proving that if a polynomial of $n$ variables is zero on an "$n$-dimensional cube", it's zero everywhere.
Nov
3
comment How to prove that $f(x)=x^{x^x}$ is strictly increasing without calculating the derivative?
@ZubinMukerjee $x^{y^z}$ is always $x^{\left(y^z\right)}$ because $\left(x^y\right)^z$ can be written as $x^{yz}$.
Nov
3
comment How to prove that $f(x)=x^{x^x}$ is strictly increasing without calculating the derivative?
@gebruiker : The function probably isn't meant to be defined at $x=0$. Please avoid changing the semantics of a question when editing it.
Nov
2
comment What is cos and sin ACTUALLY doing?
This might help: math.stackexchange.com/questions/349143/…
Nov
2
comment How to prove that something is or isn't a function of something else?
You could say that there is a free instance of $X$ in $Y_2$. Would you want $Y_3=X-X\equiv 0$ to be a function of $X$ or not?
Oct
30
comment Prove true or false that if $\sum_{n=1}^\infty{a_n}$ is absolutely convergent,
Well you could say $\sum a_n$ is absolutely convergent so $\sum |a_n|$ converges. Since $\forall x,|\sin x| \le 1$, $\forall n, |a_n \sin a_n| \le |a_n|$ so by the direct comparison test, $\sum |a_n \sin a_n|$ converges, i.e., $\sum a_n \sin a_n$ is absolutely convergent.
Oct
30
comment Prove true or false that if $\sum_{n=1}^\infty{a_n}$ is absolutely convergent,
Can't you just say $|\sin x| \le 1$?
Oct
26
comment Proof that $\mathbb{R}$ with standard topology is not a union of disjoint segments.
@mookid : Right >_<
Oct
24
comment Give an example of an infinite non-commutative ring R with char(R)=15
@MartinBrandenburg : $\mathbb Z/15\mathbb Z$-modules then.
Oct
24
comment Give an example of an infinite non-commutative ring R with char(R)=15
@MartinBrandenburg : Vector spaces.
Oct
24
answered Give an example of an infinite non-commutative ring R with char(R)=15
Oct
23
comment Can this convergent series be generalised?
$\sum\limits_{n=1}^{+\infty}\cfrac{1}{\sum\limits_{k=1}^nk!}$