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Jan
9
comment Closure of a region and shortest path
Just making sure I understand: Do you mean $\Omega$ is the 'right side' of the fattened since curve?
Jan
9
comment Closure of a region and shortest path
$\Omega$ is path connected since it is open and connected.
Jan
9
answered Proximal operators on Balls (Projection)
Jan
9
comment The value of $P\bigl(|X-Y|>6\bigr)$
Are $X,Y$ normal?
Jan
9
comment Metric on function space for Pointwise Convergence
No to metric (see ams.org/journals/proc/1951-002-01/S0002-9939-1951-0040647-7/…), yes to topology (weak topology).
Jan
8
comment When to write “$dx$” in differentiation
Thanks for some sanity...
Jan
8
revised When to write “$dx$” in differentiation
get rid of the partials
Jan
8
comment When to write “$dx$” in differentiation
You are correct, of course. But it may help the OP to realise that she/he is doing calculus without her/his seat belt fastened...
Jan
8
comment When to write “$dx$” in differentiation
I assume you are not referring to forms or infinitesimals here. How do you define the terms $dx,dy$? Personally, I think the notation is horrendous (in a calculus context) and introduces more issues than it resolves...
Jan
8
comment When to write “$dx$” in differentiation
I would say that it is probably sloppy notation. I presume we're not talking differential forms here?
Jan
8
comment Where does the rotation matrix come from?
Take the unit vectors $(1,0),(0,1)$ and rotate them in the plane by an angle $x$. Then you can figure out the matrix $R$ from its actions on this basis.
Jan
8
revised Intersection of a sphere and a plane
added 235 characters in body
Jan
8
comment Intersection of a sphere and a plane
Thanks! Will be plagiarising your code for future visualisations :-).
Jan
8
comment Intersection of a sphere and a plane
+1: Nice visualisation. How did you do it?
Jan
8
answered Intersection of a sphere and a plane
Jan
8
comment Is there any way to get convergent series if I know the sum?
If $S$ is the sum, take the series $S,0,0,0,...$. Then the sum is $S$.
Jan
8
comment Designing a circuit to verify operation of an OR gate.
It is not clear what you are trying to do. Are you trying to test for all inputs, or just a particular sort of fault? If not working implies that a 1 is generated instead of 0, then you need only check $a= b=0$ and if $f=1$ then the gate fails (since this is the only input combination that produces a 0).
Jan
8
comment How to show that $B^{-1}\cdot A^{-1}=B\cdot A$?
If $A^2 B^2 =I$ then $B^2 A^2 = I$.
Jan
8
comment How do i prove this inequality
There must be something wrong with your first inequality. Missing some $n^2$s?
Jan
8
answered Prove/disprove that $\sum_0^\infty a_nx^n = 0 \rightarrow a_n = 0 \text{ for all }n$ given $|x|<1$