11,282 reputation
2849
bio website math.rochester.edu/people/…
location Rochester, NY
age 25
visits member for 2 years, 1 month
seen 11 hours ago

I'm a graduate student at the U of R in Rochester, NY. I enjoy recreational mathematics including problem solving and most things topology.


13h
comment Does an interval have a countinuous boundary
@PVAL: what is the definition of boundary you are using? I think most people would consider it $\{0,1\}$.
16h
reviewed Approve suggested edit on Proving an identity from a dilogarithm function.
Oct
26
comment If $\ker(f) \neq \{0\}$, then $f(G)$ is abelian
@Praphulka: of course, that is why I mentioned the possibility Sylow theory hadn't been covered. Still a fact the OP might find interesting.
Oct
25
comment If $\ker(f) \neq \{0\}$, then $f(G)$ is abelian
You might not have it in your class, but it follows from Sylow theory. The group $G$ is isomorphic to $\Bbb Z/3\Bbb Z\times \Bbb Z/5\Bbb Z$, which in turn, is isomorphic to $\Bbb Z/15\Bbb Z$.
Oct
25
comment If $\ker(f) \neq \{0\}$, then $f(G)$ is abelian
Is it necessary the kernel be nontrivial? It seems to me that the only group of order $15$ is cyclic, so not only is $f(G)$ abelian, but it is cyclic, too.
Oct
25
comment Show that it is at most countable
@MaryStar: if there are uncountable many $A_i$ of positive measure, then there are at least countably many with $\mu(A_i)\geq 1/n$. Since $1/n\leq\mu(A_i)$, we can add up the countably many $A_i$ we chose. Since the $A_i$ are disjoint, we have $\sum\mu(A_i)=\mu(\bigcup A_i)\leq\mu(X).$
Oct
24
comment Show :$\{B_n^2\}\to0\implies \{B_n\}\to0$.
Should we take $B$ to be a sequence? That is, do you mean $\lim_{n\to\infty}b_n^2=0$ implies $\lim_{n\to\infty}b_n=0$?
Oct
23
comment Integrating $\int_0^\infty \frac{\log x}{(1+x)^3}\,\operatorname d\!x$ using residues
@mrf: I wholly agree. I wondered the same thing, but alas, I'll let the thread continue to lie in its current state.
Oct
22
comment A proof of a small topological lemma
Everything you have done seems perfectly fine to me. Great work!
Oct
22
comment What is the incorrect proof by Euler that $\pi = 0$ (or something like that)?
math.stackexchange.com/questions/12906/is-value-of-pi-4 Is what I had in mind.
Oct
22
comment What is the incorrect proof by Euler that $\pi = 0$ (or something like that)?
I've heard of false proofs that show $1+2+3+\cdots=-1/12$ or an incorrect limit showing $\pi=2$, but I have never heard of a false proof that $\pi=0$.
Oct
22
answered Question about $e^x$
Oct
22
reviewed Close Why have we made a function to be many to one and not one to many?
Oct
22
reviewed Close Abstract Algebra and Chess
Oct
22
reviewed Close How to calculate this kind of integral?
Oct
22
comment How do I prove that $\sum_{k=1}^{b-1} [k \frac{a}{b}] = \frac{(a-1)(b-1)}{2}$?
@rogerl: care to explain? I calculate $1$ on both sides of the equation.
Oct
21
answered Find the Laurent series of $f(z) = \frac{1}{z-2} + \frac{1}{z-3}$ for $2 < |z| < 3$ and for $|z| > 3$
Oct
21
comment Construct a Compact set of Real numbers whose limit points form a countable set
Does countable include the possibility of finite? I would say your example depends on what counts as being countable.
Oct
21
answered Question on order of elements in groups (subgroups)
Oct
20
comment Why exactly is this injective? Algebraic Topology.
My apologies, I assumed you had proven the sequence was exact and was just asking why it must be the inclusion.