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olivier dot begassat dot cours at gmail dot com


Jul
18
comment The standard role of intuitive numbers in the foundations of mathematics
As one of my teachers once said (in french) "even Bourbaki's Théorie des ensembles's sections are numbered 1,2,3 etc..." We can all count; whatever happens, even if set theory is shown to be inconsistent, numbers will still exist, people (and machines) will still be able to count up to whatever. Natural numbers exist regardless of Peano axioms and ZFC, because of simple rules we are all taught as children. Much effort has gone into formalizing their properties; the axiomatic systems our ancestors have devised are richer than the mere natural numbers. But we can still count to 15 in any case.
Jul
18
comment How is $\text{End}(M)$ a ring?
@RghtHndSd thanks!
Jul
18
comment How is $\text{End}(M)$ a ring?
How do you use $$...$$ effectively in the >! environment? Can someone remove the superfluous \ from the hidden text?
Jul
18
revised How is $\text{End}(M)$ a ring?
added 296 characters in body
Jul
18
answered How is $\text{End}(M)$ a ring?
Jul
17
answered Ext functor commutes with connecting homomorphisms?
Jul
15
comment Homotopy limits
I guessed {\em ...} stood for emphasis, please correct if I misinterpreted you.
Jul
15
revised Homotopy limits
deleted 4 characters in body
Jul
3
answered Is the Reversion map in Geometric Algebra well-defined?
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
29
comment Linear Algebra without Matrices
Matrices allow you to make calculations mechanical, and to state results concisely. There are definite instances where matrices save you times and ink.
Jun
27
comment Topologies on n-manifolds
Do you mean wether it is useful of even necessary to study general topology before learning about manifolds? I don't think so, at least if you are well acquainted with calculus and euclidean space. But you should know a little about compactness, and probably about covering space theory at some point.
Jun
27
comment Exact Sequences of R-Modules
This question is missing a lot of context. What are the maps? What is $E$?
Jun
26
revised Interpretation of $p$-forms
added 15 characters in body
Jun
26
comment Existence of $p \times p $ matrices $A$ and $B$ over the field $\mathbb F_p$, $p$ prime, such that $AB-BA=I$.
A related question math.stackexchange.com/questions/125219/… The answer is YES, but I don't know the proof, and it's not straightforward (at least the original proof isn't).
Jun
26
revised Interpretation of $p$-forms
added 75 characters in body
Jun
26
answered Interpretation of $p$-forms
Jun
25
comment Canonical orientation of a complex manifold
The orientation is different for even $n$. The second choice may have the added advantage that the transition matrices are bloc matrices with blocs of the form $$\begin{pmatrix} a&-b\\b&a\end{pmatrix}$$ and so identifies nicely with complex $n\times n$ matrices.
Jun
24
reviewed Reject suggested edit on $\pi_1 (x,y) = x$ the projection function with $\pi_1 : R^2 \rightarrow R$