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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 $0<p<1$ when endowed on $C[0,1]$
Is the power of the integral purposely $2p$ or should it be $\frac{1}{p}$?
Sep
11
accepted Is the sum of the diagonals of an isosceles trapezoid at least the sum of the bases?
Sep
11
comment Is the sum of the diagonals of an isosceles trapezoid at least the sum of the bases?
That's a really nice and clear way to see it. Thanks.
Sep
11
comment Is the sum of the diagonals of an isosceles trapezoid at least the sum of the bases?
@Sigur: Do you mean the triangle inequality? I hadn't so far, but if $a,b$ are bases and $c$ the leg, $d$ the diagonal, then triangle inequality would give $a+b\leq c+d+c+d=2d+2c$. The $2c$ kind of ruins it:( Or did I misunderstand your point?
Sep
11
asked Is the sum of the diagonals of an isosceles trapezoid at least the sum of the bases?
Aug
31
comment How to construct a one-to one correspondence between$\left [ 0,1 \right ]\bigcup \left [ 2,3 \right ]\bigcup ..$ and $\left [ 0,1 \right ]$
@AsafKaragila: Just out of curiosity, what argument did you have in mind that would contradict continuity from this union set to $[0,1]$?
Aug
27
comment How to strictly mathematically prove that definition is wrong?
What do you mean by proving that $5=4$? What is $5$?
Aug
27
answered Does a compact subspace need to be closed?
Aug
24
comment the function $1/|x|^α$ in $R^n$
@BR. Thanks, that makes it a lot more clear.