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location Toulouse
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visits member for 3 years, 7 months
seen Aug 26 at 17:48

Jun
13
comment When are configuration spaces aspherical?
Would you mind giving a reference for Fox-Neuwirth theorem, please? I can't find it with Google.
Apr
2
comment “Natural” pairings between exterior powers of a vector space and its dual
If i understand [differential forms and integrals] well, to integrate a differential form with the first pairing, one needs to cut the space into rectangles/parallelepipeds, and with the second pairing, one needs to cut the space into triangles/tetrahedra. :)
Dec
26
comment Why do we teach calculus students the derivative as a limit?
"What benefit is there in introducing to calculus students the $h→0$ definition of a derivative?" -- you have to define it anyway, don't you? I agree that calculating a derivative of something like $x\mapsto 3x^2$ by definition can be boring, it is better to ask a student to derive the product or the quotient rule for the derivative, for example.
Dec
13
revised Compactness of the Hilbert cube without the Axiom of Choice
clarify the choice function F
Dec
13
accepted Compactness of the Hilbert cube without the Axiom of Choice
Dec
13
answered Compactness of the Hilbert cube without the Axiom of Choice
Dec
13
awarded  Popular Question
Dec
5
revised Formal languages with non-unique interpretations of terms
add a paragraph with some clarifications of my motivations
Dec
5
comment Formal languages with non-unique interpretations of terms
Thanks for the link. I haven't thought of multivalued functions, but one of the things that motivated my question was my impression (i am not sure and have no reference) that in the first half of the nineteenth century, in model theory or mathematical logics texts, the equality was not always interpreted as the identity, but only as an equivalence relation. Sometimes (as mentioned by François Dorais) the equivalence relation could be the one of a rewriting system.
Dec
4
comment Formal languages with non-unique interpretations of terms
@EmilJeřábek, i understand well that the equality relation is not symmetric with the $\omicron/O$ notation, this is one of the first things i tell my students. However, my impression was that it is a secondary concern, and can be addressed after the ambiguity of the notation is addressed. I felt that multi-valued interpretations are better than interpretations by sets because they would generalize the usual interpretation instead of replacing it with a new one (no need to interpret $\ln(2x)=\ln2 +\ln x =O(\ln x),\ x\to\infty$ as two relations between sets of functions).
Dec
4
asked Formal languages with non-unique interpretations of terms
Jul
2
awarded  Curious
Jun
14
comment Atiyah-MacDonald, exercise 2.11
Is Cayley-Hamilton Theorem necessary here? Is there no easier way to show that the powers of $\phi$ are linearly dependent over $A$?
May
26
revised Topological characterization of the closed interval $[0,1]$
grammar
May
26
accepted Topological characterization of the closed interval $[0,1]$
May
25
comment Topological characterization of the closed interval $[0,1]$
In other words, in some sense, $[0,1]$ is the "simplest" non-trivial absolute retract.
May
25
answered Topological characterization of the closed interval $[0,1]$
May
23
awarded  Organizer
May
23
revised Defining Multiplication in Polynomials over Rings of Matrices
add [reference-request] tag
May
23
suggested approved edit on Defining Multiplication in Polynomials over Rings of Matrices