bio | website | |
---|---|---|
location | Argentina | |
age | ||
visits | member for | 4 years, 7 months |
seen | Sep 12 at 19:22 | |
stats | profile views | 653 |
email: [the shortest string of letters containing my first name and last name as substrings]@gmail.com
Sep 12 |
comment |
Does anyone know an intuitive proof of the Birkhoff ergodic theorem?
If $f\equiv 1$ and $T=I$ we have $M_T'\equiv+\infty$, so the recurrence formula is $+\infty + f=+\infty$, which is useless. Am I missing something? |
Aug 23 |
awarded | Nice Answer |
Aug 12 |
revised |
real symmetric matrix has real eigenvalues - elementary proof
added 391 characters in body |
Aug 12 |
revised |
real symmetric matrix has real eigenvalues - elementary proof
added 391 characters in body |
Aug 12 |
revised |
real symmetric matrix has real eigenvalues - elementary proof
added 391 characters in body |
Aug 6 |
revised |
real symmetric matrix has real eigenvalues - elementary proof
added 1 character in body |
May 28 |
awarded | Necromancer |
May 27 |
awarded | Yearling |
May 27 |
answered | Can the unsolvability of quintics be seen in the geometry of the icosahedron? |
May 6 |
awarded | Popular Question |
Dec 16 |
awarded | Nice Answer |
Jul 29 |
awarded | Nice Question |
Jun 25 |
awarded | Excavator |
Apr 19 |
comment |
Giving $Top(X,Y)$ an appropriate topology
For the non-Hausdorff case, see ncatlab.org/nlab/show/exponential+law+for+spaces. |
Mar 8 |
comment |
Topological spaces determined by generalized metric spaces
Notice that this Arens' space is slightly different from the one given in Wikipedia (en.wikipedia.org/wiki/Arens%E2%80%93Fort_space), since in this space the set $\{c\}\cup\{a_{n,m}:n,m\in\omega\}$ is not open. |
Feb 20 |
awarded | Yearling |
Jan 25 |
asked | Nontrivial copies of SO(r) in SO(n) |
Jan 24 |
comment |
Suggestions for good notation
@Ben, the index in the coordinate expression $\frac{\partial f}{\partial x^j}$ for the 1-form $df$ is clearly in the low position! In fact, this is the main reason that I see for having to put the indexes of the coordinates in the high position as we do, instead of doing everything in the opposite way, which would be better in some way: we could write $f=x_1^2+x_3$ instead of $f=(x^1)^2+x^3$. |
Jan 24 |
comment |
Suggestions for good notation
Regarding differential geometry: If $f:M\to\mathbb R$ is a smooth function on a manifold and $x:M\to\mathbb R^n$ is a chart, I prefer $\left(\frac{\partial f}{\partial x}\right)_j$ or $\left(\frac\partial{\partial x}\right)_j f$ (or even $\partial_j f$ if the choice of the particular chart is clear or irrelevant). Because the notation $\frac{\partial f}{\partial x^j}$ suggests that $\frac{\partial f}{\partial g}$ could be defined using only $g$, and in fact you need to know that you are restricting to the curve along which the other coordinates $x^i$ are constant. |
Jan 21 |
revised |
Why is a topology made up of 'open' sets?
added 111 characters in body |