bio | website | |
---|---|---|
location | Toulouse | |
age | ||
visits | member for | 3 years, 3 months |
seen | Apr 12 at 9:17 | |
stats | profile views | 338 |
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 |
May 10 |
revised |
Vector bundles vs principal $G$-bundles
remove "G-bundle", leave "principal G-bundle", as this is what is described |