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olivier dot begassat dot cours at gmail dot com


Nov
6
answered Does every set have a derangement?
Nov
4
comment Given three non abelian group of order 8,two must be isomorphic.
It is true, and a good exercise too.
Nov
3
reviewed Close How to determine if the subset is closed under scalar multiplication and vector addition
Nov
3
reviewed Close Prove there exist sets $A, B, C, D$ with $(A \cup C) × (B \cup D) \not = (A × B) \cup (C × D)$
Nov
3
reviewed Close Confusions about Linear Algebra (determinants)
Oct
31
comment Connected spaces of $M(n,\mathbb R)$
This is discussed in en.wikipedia.org/wiki/…, but no details are given unfortunately.
Oct
31
comment Connected spaces of $M(n,\mathbb R)$
I learnt all of this in french books... Do you read french?
Oct
31
comment Connected spaces of $M(n,\mathbb R)$
part (c) is elementary matrix manipulations. It is a theorem that these types of matrices generate $SL_n$.
Oct
31
answered Connected spaces of $M(n,\mathbb R)$
Oct
29
comment Borel Measures: Atoms (Summary)
It relies on the underlying set being numerable to prove that the equivalence class is in $\Sigma$, and some form of countable choice to represent the equivalence class as a countable intersection of measurble sets.
Oct
29
comment Borel Measures: Atoms (Summary)
You could try something along the lines of considering the equivalence classes under the equivalence relation $x\sim y$ iff for any $A\in\Sigma$, $x\in A\Longleftrightarrow y\in A$. If this works then the equivalence classes are the smallest measurable sets, and define the smallest measurable partition.
Oct
29
comment Solution verification: $G$ and $G/H$ contain elements of same order
The correct formula is $$|G/H|=\frac{|G|}{|H|}$$ at least for finite groups, and there are non-isomorphic groups of the same order, so your argument is incorrect on two fronts.
Oct
28
comment Sam Harris' theory of probability on the Second Coming of Christ
@GrumpyParsnip I don't think dei could produce a rock that dei couldn't lift deiself, but dei may ask deis deity friends to make one for deis.
Oct
28
comment Sam Harris' theory of probability on the Second Coming of Christ
I watched that interview a few days ago, and was in total agreement with Sam Harris on his probability argument. I'm quite amused this question found its way to this forum, @SteveMcQueen are you per chance trying to settle some internet dispute?
Oct
26
revised If $A$ is connected, is at least one of the sets $\mathrm{Int}A$ and $\mathrm{Bd}A$ connected?
added 50 characters in body
Oct
26
comment If $A$ is connected, is at least one of the sets $\mathrm{Int}A$ and $\mathrm{Bd}A$ connected?
@DanielFischer You are right. I'll correct that.
Oct
26
answered If $A$ is connected, is at least one of the sets $\mathrm{Int}A$ and $\mathrm{Bd}A$ connected?
Oct
26
comment Topology on $C_{compact}^{\infty}(R)$
Are you equipping the $C^\infty(K)$, $K$ compact, with the topology defined by the family of semi-norms $$\|f\|_m=\sup_{x\in K}|f^{(m)}(x)|\;?$$
Oct
26
comment Topology on $C_{compact}^{\infty}(R)$
Equipped with what topology?
Oct
26
comment Topology on $C_{compact}^{\infty}(R)$
What is a "good semi-norm"?