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Doing math.


Dec
6
answered Proof for Image of Indexed Collection of Sets?
Sep
24
comment How to apply Borel-Cantelli Lemma here?
I edited it to have homework tag. Correct me if I'm wrong.
Sep
24
revised How to apply Borel-Cantelli Lemma here?
edited tags
Aug
28
comment A set $A$ is closed iff $\operatorname{fr}A\subseteq A$.
@Citizen. What definition of an exterior point do you use then?
Aug
28
comment A set $A$ is closed iff $\operatorname{fr}A\subseteq A$.
is $Fr(A)$ the closure of $A$?
Aug
28
answered How can I prove that this set is finite?
Aug
23
revised When is the logarithm of this function square integrable?
edited title
May
19
awarded  Constituent
May
7
awarded  Caucus
Mar
21
comment “Maximal” sets with cardinality $\aleph_0$?
Few comments and questions: 1. What do you mean by being dense in itself? Dense in its own subspace topology? In this sense every set is dense in itself. 2. Denseness is a topological property. Saying that $\mathbb{Q}$ is more dense or less dense doesn't make sense: it either is dense (in some superset) or it isn't.
Mar
20
comment Set of Continuous Functions, Functionals, and Equicontinuity
What are your thoughts on this problem? Have you tried anything?
Mar
14
comment I thought I proved the Limit here didn't exist…
Note that $\sqrt{2x^{2}}=|x|\sqrt{2}$ and not $x\sqrt{2}$.
Mar
13
comment Cantor Function Question
@AsafKaragila: I'm guessing that he might mean the following. Some analysis textbooks define the Cantor function by defining it as constant pieces outside the Cantor set (in the open intervals that were removed at each step), and then inside the Cantor set by limits. In this case, you don't get any expression of the function inside the Cantor set, but only in its complement.
Mar
13
comment Cantor Function Question
Congrats for 1,000 answers.
Mar
13
comment How is Hausdorff Distance sensitive to position?
I only mentioned that condition in order to avoid writing concrete counter-examples. However, the shortest distance also fails to satisfy the triangle-inequality. Take $A=[0,1]$, $B=[2,3]$, and $C=[4,5]$ as a simple example. By shortest distance, $d(A,C)>d(A,B)+d(B,C)$, since $3>2$. I don't think the triangle inequality is negotiable when defining metric spaces. What is there left, the symmetry?
Mar
13
comment How is Hausdorff Distance sensitive to position?
A small note to the second sentence in the last paragraph: the shortest distance is not actually a metric. It fails to satisfy e.g. the condition $d(A,B)=0\Leftrightarrow A=B$.
Mar
13
revised condition $\mu ^*(B\cup C)=\mu ^*(B)+\mu ^*(C)$
added 45 characters in body
Mar
13
answered condition $\mu ^*(B\cup C)=\mu ^*(B)+\mu ^*(C)$
Mar
13
comment Is there really no way to integrate $e^{-x^2}$?
You probably mean that any continuous function is Riemann integrable on a compact interval.
Mar
12
comment Trying to define $\mathbb{R}^{0.5}$ topologically
Thanks! Interesting way of looking at it.