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Aug
29
answered Is the graph of $xy=1$ in $\mathbb C^{2}$ connected?
Aug
29
revised Two disjoint compact sets in a topological group
added 15 characters in body
Aug
29
answered Two disjoint compact sets in a topological group
Aug
29
comment Two disjoint compact sets in a topological group
You forgot to reqwuire that $V$ is not empty, I suppose
Aug
29
comment Finding $|E|$, where $E$ is the Splitting Field of $x^8-1$ over a Field of $4$ Elements.
It is well-known that there is no $i$ in team, but there is also no $i$ in characteristic $2$ ...
Aug
29
comment Is every axiom in the definition of a vector space necessary?
@Vim Actually, one axiom is enough: A vector space is an abelian group on which a field acts. :)
Aug
29
comment Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
@pooja Let $a$ be any reflection, let $c$ be any rotation. Find $b$ such that $ab=c$. Is $b$ a reflection or a rotation?
Aug
29
answered Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
Aug
29
comment Bounded sequence in a metric space
While this shows that we could base everything on closed balls, we usually argue with open balls only - and be it to avoid that you accidentally use the closed ball of radius $0$.
Aug
28
answered Show that $f(n)$ is $O(g(n))$ then $f(n)+c$ is $O(g(n))$
Aug
28
comment Find all functions f such that $f(f(x))=f(x)+x$
There's no need to assume surjectivity. Injectivity follows readily and your $(4)$ for $a,b>0$ shows (using continuity) that $[0,\infty)$ is in the image. As $x\mapsto-f(-x)$ also has the given property, we conclude that also $(-\infty,0]$ is in the image. (This also shows we need only consider $a>0$)
Aug
28
comment Find all functions f such that $f(f(x))=f(x)+x$
Pfft, continuous is lame. ;)
Aug
28
comment Proving that $a^{b}$ is rational (Elementary number theorey)
I hate to tell this, but your argument is almost totally unrelated to the claim, as it begins with an erroneous contraposition
Aug
28
comment When can a set have an upper bound but no least upper bound?
Try $\emptyset$
Aug
28
comment Find all functions f such that $f(f(x))=f(x)+x$
These should be all $\mathbb Q$-linear solutions. My solution set overlaps with @Michael's, but neither solution set is contained in the other.
Aug
28
answered Find all functions f such that $f(f(x))=f(x)+x$
Aug
28
comment Can math be subjective?
like this, not like this. Of course the method is the same, but I really have difficulties "to adapt my eyes"
Aug
28
comment Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
This is in fact a nice idea, but I think one needs a bit more care to elaborate such an "equilibrum" argument to work with several resdistribution steps. At which moment you certainly exceed thet complexity of Barry Cipra's argument.
Aug
28
comment Limit of sequence of real numbers
monotone is not needed, $m(n)\to\infty$ should be enough (and would possibly match the OP's notion "$m\to\infty$ as $n\to\infty$")
Aug
28
awarded  Good Answer