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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.
Aug
24
comment the function $1/|x|^α$ in $R^n$
If $f:\mathbb{R}^{n}\to\mathbb{R}$, then what does $f(r)$ mean for $r\in[0,\infty[$?
Aug
23
answered Question about measurable sets $E_n$ such that $\lim_{n\rightarrow \infty}L^N(E_n) = 0$.
Aug
17
comment 2 jars with 50 balls each. Pick any ball with $>50\%$ probability.
@sTEAK. If you take one from each jar then the probability of getting a red is $1$.
Aug
16
comment Is it possible to have $D=\Bbb P$
@t.b. Yeah, the countability is important :) Baire implies that any countable completely metrizable topological space has an isolated point. If not, you could write the whole space as a countable union of nowhere dense closed sets (singletons), making the whole space to have an empty interior, which is a contradiction.
Aug
16
comment Is it possible to have $D=\Bbb P$
@t.b. Yeah, I meant an isolated point. And true, that also does the job. Thanks for providing an alternative way of seeing it.
Aug
16
revised Is it possible to have $D=\Bbb P$
added 462 characters in body
Aug
16
answered Is it possible to have $D=\Bbb P$
Aug
14
comment Is the set of irrationals separable as a subspace of the real line?
@CameronBuie. To add on Asaf's comment, it's worth noting that the word 'metric space' plays a key role there. Metrizability is hereditary and so is second countability. Since in a metric space separability (also Lindelöf) is equivalent with second countability, then every subspace of a separable metric space is separable (and Lindelöf, for that matter).