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age 23
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Doing math.


Jul
2
awarded  Curious
May
28
comment Research Area Choice: PDE vs Optimization
What type of industry would you like to consider outside of academia? Bear in mind that PDEs are used in finance too.
May
15
comment How to prove or disprove $P(\overline A) = P(U) - P(A)$
Could you clarify what $P(A)$ stands for? And what exactly do you mean by the statement "$U-A$ implies $A\cap \overline{U}$"?
May
15
comment Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable.
@user140794: Assume that there are infinitely many $a_{1},a_{2},...\in A$ with $f(a_{k})>\frac{1}{n}$ for all $k\in\mathbb{N}$. Then $\sup_{N\in\mathbb{N}}\sum_{k=1}^{N}f(a_{k})=\infty$, which is a contradiction to your assumption. And note for the last part: for absolutely convergent series the order of terms doesn't affect the sum.
May
14
answered Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable.
May
13
answered Any idea of how to prove this
May
13
comment A subspace of a separable metric space is separable
The goal is not to show that $A$ is dense and countable, as this would not necessarily be true, but rather that $A$ contains a countable dense subset of itself with respect to the subspace topology.
May
13
revised Proving that there is no norm for the space of real-valued sequences making it a complete metric space.
edited tags
May
13
comment Geometric meaning of symmetric connection
Have you computed both sides of $(2)$ for the Euclidean connection on $\mathbb{R}^{n}$?
May
13
revised Motivation of vector bundle of a manifold
edited tags
May
13
answered Motivation of vector bundle of a manifold
May
11
comment Equivalent definitions of vector field
@soporhs. You're welcome. I'll gladly answer any questions you might have, but I advice that you try to work the details on your own at first.
May
11
revised Equivalent definitions of vector field
added 84 characters in body
May
11
comment Equivalent definitions of vector field
What definition of $TM$ are you working with? It seems that this answer only opens the usual definition of the tangent space but I can't see how you identify those two definitions of a vector field.
May
11
answered Equivalent definitions of vector field
May
11
comment Equivalent definitions of vector field
What is your definition of $TM$?
May
6
comment $\mathbb R$ has the same cardinality of any interval
$g$ is not defined at $x=-1$.
May
6
answered Openess of sets given by equivalence relations in the quotient topology.
May
2
comment $L^p$ not sequentially compact
Didn't you just show there that $\lim_{n\to\infty}\sqrt{sin(n\pi x)}= 0$ in the $L^{2}$ topology? Every subsequence of this sequence converges in $L^{2}$, so how is this a counter example?
May
2
answered Closure open ball