Reputation
6,207
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
18 35
Newest
 Explainer
Impact
~188k people reached

1d
comment Closed subset for $L^2$ strong and weak convergence
Yep, you are in the right track.
1d
comment Closed subset for $L^2$ strong and weak convergence
Do you know the weak limit of $f_n(x) = \sin(nx)$? If so, try to find a similar sequence with $f_n(x) \in K=\{-1,1\}$.
Feb
4
comment Justify or provide counterexamples
My point is, that the function is equal to $e^{-x}$ (almost everywhere which is true equality in the space $L^1$). Hence, it is not an example since $e^{-x}\to 0$.
Feb
4
answered Justify or provide counterexamples
Feb
4
comment Justify or provide counterexamples
Strictly speaking your example in (i) is not a counterexample, as it is the same function as $e^{-x}$ (in $L^1$).
Feb
4
comment Mentally approximating an inverse sine?
I don't know what unit you use. It's $\pi/2$ for radiants, $180$ for degree.
Feb
4
comment Mentally approximating an inverse sine?
$\sin(x) = \cos(x + c)$ ($c$ depending if radiants, degree or whatever). Hence, for the inverse (on appropriate domains): $\sin^{-1}(x) = \cos^{-1}(x)-c$.
Jan
27
comment What is wrong with my contradiction?
Something to memorize: Induction shows the result for an arbitrarily large number of summands. But "arbitrarily large" is still not quite infinity.
Jan
20
revised why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem?
added 22 characters in body
Jan
2
answered why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem?
Dec
20
reviewed Close can't understand proof for the law of tangents
Dec
20
reviewed Leave Open Show that $\lim\limits_{r\to\infty} \textrm{\{} \|x-ru\|-\|y-ru\| \textrm{}\} = \left<y-x,u\right>$
Dec
20
reviewed Close Example of a series, which its square sum converges, but it is not a Cauchy sequence.
Dec
15
awarded  Explainer
Dec
15
revised Derivative of 1-norm
edited title
Dec
15
answered Derivative of 1-norm
Dec
14
reviewed Leave Open Is there a surjective group homomorphism $GL_{n}(k) \to GL_{m}(k)$ where $n > m$?
Dec
14
reviewed Close The relation between face counts and edge counts in a polyhedron, $3f_3 + 4f_4 + 5f_5 +\dots = 2E$
Dec
9
comment What comes after geometric mean?
Other problems besides non commutativity are that the $n$-th super root does not always exists (even for positive arguments) and that it is in general multivalued (and even two different positive super roots can occur).
Dec
9
answered Taking the means of numbers repeatedly