5,511 reputation
1622
bio website xavierm02.net
location France
age 21
visits member for 3 years, 7 months
seen 12 hours ago

Dec
16
comment Theorem proving skills in calculus, clearer idea to read in reverse order; linear-reading with writing down helps little
I think you're not supposed to remember the proofs by heart. You should do a lot of exercises, which with increase you confidence and speed when tackling problems of a given subject and remember proofs by their tricky part. Most of the time, a hard-to-remember proof begins by some construction that seems like it comes out of nowhere and then the proof is just a verification that it indeed has the right properties. So just remember the stuff that feels like it's coming out of nowhere and, if you have done enough exercises, you should be able to fill in the blanks.
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 $y=0$.
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.