Good evening (London) everyone, Random question which I felt shy to ask on meta..but what does a +1 and a "removed" message on an answer I posted a while back mean?
@JasperLoy basically I only thought the rep score for answers were +10 or -2 but I had a score of +1? But not to worry I was looking for a quick answer :).
My best friend will be returning next month from Oxford, have not seen him for years.
@Sarah I dislike the idea of using the internet on phones. I am on my laptop now. I decided to move my desktop to the store room to have more space on my desk.
@Sarah OK. I think I won't log in to the site next year. I will be busy studying my 12 holy books. Then I can take the GRE in 2016 and enter grad school in 2017.
Can anyone think of a function $f:A->R$ that has countably infinite essential discontinuities ? By $p \in A$ being an essential discontinuity of f, i mean that either lateral limits of f don't exist at p.
@JasperLoy do you know of an extremely simple proof that the alternating group $A_4$ doesn't have a subgroup of order $6$ for someone who only knows group theory for a few days
There have been a number of discussions about "pity" or "sympathy" upvotes.
http://meta.stackexchange.com/search?q=pity+sympathy+upvote
That is, the idea that once a post is voted down to -1, some kind-hearted user will come by and upvote the post, no matter how terrible or wrong it may be, to ...
I know, this may sound like it is off-topic, but hear me out.
At Stack Overflow and here we get votes on posts, this is all stored in a tabular form.
E.g.:
post id voter id vote type datetime
------- -------- --------- --------
10 1 2 2000...
This sum $$\sum^\infty_{n=1}\frac{(-1)^nH_n}{n^4}$$ can be done elementarily, no need for complex analysis. Besides that, my master formula also emphasizes the relation between $$\sum^\infty_{n=1}\frac{(-1)^nH_n}{n^4}$$
and $$\sum^\infty_{n=1}\frac{H_n}{2^4 n^4}$$ in a generalized form since this is just a particular case.
For a metric space $X$, what are the conditions on $A \subset X$ for $A' = X \setminus A$ to be open? Simmons wants me to prove this for finite $A$ and that is obvious enough by picking up a $r < d(x, A)$, $S_r(x)$ being the desired open spheres around $x$. But I am sure there can also be infinite $A$s for which $A'$ is opne, no? @DanielFischer
Above, the last sum is $$\sum^\infty_{n=1}\frac{H_n}{2^n n^4}$$
@robjohn it's interesting to check in the next period of time what is the best proof for $$\sum^\infty_{n=1}\frac{H_n}{2^n n^3}$$ Well, I can easily finish it by using the generating functions, but I can also do it by other means. I don't think I have a very clever proof like one line proof yet.
@DanielFischer Some of the exercises in Simmons are very lame (while some are equally good). For example, the next exercise wants me to prove that every subset of a metric space $X$ is open $\iff$ singleton sets of $X$ are open.
It's trivially true : $(\Rightarrow)$ as singleton subsets are subsets and $(\Leftarrow)$ as every subset is union of singleton subsets and openness is invariant under taking unions.
@DanielFischer One more thing : I have to prove that given a metric space $(X, d)$, $d' = d/(1+d)$ is also a metric on $X$. Walkthrough? I don't seem to be able to prove it.
@BalarkaSen Positivity and symmetry should be obvious. The only nontrivial part is the triangle inequality. Look at the function $t \mapsto \frac{t}{1+t}$ for that.
What properties of that function might be relevant?
I know, this may sound like it is off-topic, but hear me out.
At Stack Overflow and here we get votes on posts, this is all stored in a tabular form.
E.g.:
post id voter id vote type datetime
------- -------- --------- --------
10 1 2 2000...
