T. Eskin
Reputation
4,881
Next privilege 5,000 Rep.
Approve tag wiki edits
 Nov 20 comment Some questions about First countable space and continuous function You might be mixing up first countability and second countability: First countability says that every point has a countable neighbourhood basis, while second countability says that the space has a countable base of open sets. Nov 19 comment Proving the existence of a non-decreasing sequence @thkang: The thing what Asaf is trying to point out, is that $(a_{n})$ is an arbitrary sequence satisfying the required conditions. You can't prove this theorem by choosing some particular sequence $(a_{n})$ and finding $(b_{n})$ respectively. By doing this, it only proves that it works in this special case. Nov 10 comment Show that $C([0,1],\mathbb{R})$ with the $L_2$ inner product norm is not a Hilbert space. It's not entirely correct that you need to show that every Cauchy sequence does not converge in that space, but merely, some don't. There are Cauchy sequences that do converge, you just need to find one that doesn't. Nov 10 comment Continuity from below and above Aside the word "continuity", what else exactly are you not understanding in these statements? Nov 7 comment Linear transformation such that $T^{2}v \neq 0$ and $T^{3}v = 0$. Is this question from a GRE mathematics subject test? Nov 6 answered If $A$ and $B$ are separated, is $m^*(A \cup B)=m^*(A)+m^*(B)$? Nov 6 answered Supremum of the set $M_x$ for $x\in \mathbb{R}$ Nov 6 comment Supremum of the set $M_x$ for $x\in \mathbb{R}$ You probably mean that $M_{x}$ is bounded from above, since it is not a bounded set. Oct 26 comment Why define the Cantor set with an intersection? If you want to discuss limits of subsets of the reals, I would suggest looking up "Hausdorff distance". In fact, $C$ is a limit of the sequence $(E_{n})$ in this topology. Here's a link to Wikipedia: en.wikipedia.org/wiki/Hausdorff_distance Sep 29 comment Uniform convergence of a sequence of increasing real functions Is the sequence increasing, or are each $F_{n}$ increasing? Sep 21 comment Squaring gets puzzled. @ParthKohli: That doesn't mean that $-1$ would be an answer, since the implication from right to left does not hold. Sep 11 comment $L_p$ norm not subadditive for \$0