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bio website xavierm02.net
location France
age 22
visits member for 3 years, 11 months
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Jan
23
comment $x=yx$. Can this statement be true when we don't know that $y=1$?
$yx=x \implies yx-x = 0 \implies x(y-1)=0 \implies x= 0 \text{ or } y = 1$
Jan
21
comment Finding $|a|$, a complex number, given a system of equations
Have you tried using $z\overline{z}=|z|^2$?
Jan
18
comment [Verification]$G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
a^n or a^{stuff}${}{}{}{}{}{}$
Dec
27
comment Is there any 100% sure numerical method to find all roots in a polynomial equation of degree n without fail?
The idea is that the roots are the eigenvalues of the companion matrix, and that we know how to computer the eigenvalues of a matrix numerically.
Dec
27
comment Is there any 100% sure numerical method to find all roots in a polynomial equation of degree n without fail?
See mathworld.wolfram.com/PolynomialRoots.html
Dec
20
comment Derivative of a quadratic form
Have you tried looking at an example? Like $X=\begin{pmatrix}0&i\\-i&0\end{pmatrix}?$
Dec
14
comment Basic Axiomatic Definitions in Categories and Allegories (Freyd and Scedrov)
For example $x\mapsto \cfrac{1}{x}$ isn't defined at $0$ so it's not total (as a function of $\mathbb R \to \mathbb R$). And a binary partial operation is to a binary operation what a partial function is to a function.
Dec
14
comment Basic Axiomatic Definitions in Categories and Allegories (Freyd and Scedrov)
And a binary operation is a function $f:A\times A \to A$. You can also represent a function $f:X\to Y$ by a subset $F$ of $X \times Y$ so that $\forall x\in X,\forall y_1,y_2 \in Y, (x,y_1)\in F \land (x,y_2)\in F \implies y_1 = y_2$ ([functional] given an input, you have at most one output) and $\forall x\in X, \exists y \in Y, (x,y)\in F$ ([total] given an input, you have at least one output). A partial function is like a function in the sense that it is functional but it doesn't have to be total. In other words, a partial function is a function that can't give an output on some inputs.
Dec
14
comment Basic Axiomatic Definitions in Categories and Allegories (Freyd and Scedrov)
He might represents an object $A$ by $id_A$, then it all kind of makes sense. But then, it's weird that he doesn't simplify the rules by to get, for example, $\square(xy)=\square x$ instead of $\square(xy)=\square( x(\square y))$
Dec
12
awarded  Nice Answer
Dec
10
comment How many graphs on the vertex set {1, …, 12} have exactly 15 edges?
The total number of posssible edges of a graph with $n$ vertices is $n^2$ if you allow edges from an edge to itself and $n^2 - n = n(n-1)$ otherwise.
Dec
7
comment Prove $\{g(x_n)\}_{n=1}^\infty$ converges
One way to work you way through this kind of problem is to rename everything that's small and positive to $\varepsilon_1$, $\varepsilon_2$, etc. Then, you just have to find out which ones must be equal.
Nov
30
revised A function whose graph has vertical asymptotes at $x=+2$ and $x=-2$, and a horizontal asymptote at $y=0$
added 11 characters in body
Nov
30
comment Can we build infinite products in $k[[X]]$?
What would you want it to be for $P\equiv -1$?
Nov
30
comment Is there any diffeomorphism from A to B that $f(A)=B$?
You probably tried the function $f(x)=e^{i\pi/2}x^3$. And you have the problem that at $f'(0)=0$. I suggest you try $g(x)=f(x-c)+e^{i\pi/2}c^3$ to try to push the problem outside of the domain. The only difference with $f$ is that $g$ turns around $c$ instead of turning around $0$.
Nov
27
comment proof that $a_n$ is a null sequence
That's overkill.
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 $y=0$.