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olivier dot begassat dot cours at gmail dot com


1d
comment a question about sequence and series. prove $ \lim_{n \to \infty}( n\ln n)a_{n}=0$?
Does $nlnn$ stand for $n\ln(n)$?
2d
comment Can anyone give the equation of the inverse of radial projection from a tetrahedron to sphere?
The answer will depend on the tetrahedron and how you are parametrizing it.
2d
comment Completeness of Locally Compact Metric Space and Group of Isometries
Looks good. ${}{}$
2d
comment Completeness of Locally Compact Metric Space and Group of Isometries
$(0,1)$ is a locally compact metric space...
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
15
comment Homotopy limits
I guessed {\em ...} stood for emphasis, please correct if I misinterpreted you.
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
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
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
23
comment Show $\mathbb{CP^2/CP^1}$ is not a retract of $\mathbb{CP^4/CP^1}$.
$\Bbb CP^2/\Bbb CP^1$ is homeomorphic to the $4$ sphere, and thus its cohomology ring is $\Bbb Z[t]/(t^2)$ with $t$ of degree $4$. If you use the long exact cohomology sequence $$\cdots\to \tilde{H}^*(\Bbb CP^4/\Bbb CP^1)\to H^*(\Bbb CP^4)\to H^*(\Bbb CP^1)\to \cdots$$ you can see that the cohomology ring of $\Bbb CP^4/\Bbb CP^1$ is $\Bbb Z[u,v]/(u^3,v^2,uv=vu=0)$ with $u$ in degree $4$ and $v$ in degree $6$. I'm not certain you can solve the problem only using the ring structure of cohomology.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy upon looking very carefully I did indeed see this ^^ all joking aside, I don't understand the question, but it's fine if all doubts were cleared up by your answer.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy I don't understand what is holding OP back from dividing the equality $\mathrm{tr}(g)-1=2\cos(\theta)$ by $2$...
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
... I don't understand the question.
Jun
23
comment What does “coproduct of $\Bbb{Z}*\Bbb{Z}$ of $\Bbb{Z}$ by itself” mean?
The coproduct of $X$ by itself simply means the coproduct of $X$ with $X$. The author is just explaining what they mean by $\Bbb Z*\Bbb Z$.
Jun
23
comment Notation for a vector space: $(\mathbb{C}^\infty)^{\otimes L}$
What do you mean by "countably or uncountably infinite"?
Jun
23
comment Notation for a vector space: $(\mathbb{C}^\infty)^{\otimes L}$
$\Bbb C^{\infty}$ is $$\bigoplus_{n\in\Bbb N}\Bbb C\,,$$ in other words, it's a complex vector space with numerable basis. You can describe it as the space of complex sequences that are eventually $0$.