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comment Convergence of $\int_0 ^\infty \frac {dx}{\sqrt {1+x^3}}$
@Wanderer You have been told to avoid double dollar signs in titles. Please remember to do so. Double dollar signs in title render like $$\text{ this}$$ instead of rendering like $\text{this}$ (inline). This makes titles messy in the main site. Regards,
comment Positive series problem
@Fundamental Go ahead. I won't complain.
comment Positive series problem
David, apologies in advance for changing the colour of $a_n$; but maroon is dark and close to black and it seems to upset the eyes of some people with colour issues.
revised Positive series problem
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answered Is $\text{Hom}(\prod_p \Bbb Z/p\Bbb Z, \Bbb Q) = 0$ possible without choice?
comment $\sqrt{I}+\sqrt{J}=R$ implies $I+J=R$
This has been asked before. Surf the [abstract-algebra] tag a little.
reviewed Reject Complex numbers - Exponential numbers - Proof
comment How does the Euler Totient Function apply here?
That's no necessary. List them. What are the even numbers that are $<2013$? Well, those are $2,4,\ldots,2012$ so the number is $1006$.
answered How to prove $L_{f}(P) \leq L_{f}(Q)$ when $Q$ and $P$ are partitions of $[a,b]$ and $Q \supseteq P$
comment What is your “go-to” method/style to prove convergence or divergence?
Sadly there is not one. For example, the convergence of $\sum n^{-1}\sin n$ is related to the irrationality measure of $\pi$. Series can encode deep and relevant information, and hence there is no hope for a general theorem that covers them all.
comment $\gcd(4n+1, n+2)$ is found in what sense?
The Eulclidean algorithm works for any pair integers, not only the nonnegative ones. Thus, it is irrelevant whether $n\geqslant 5$ or not.
comment Degrees of irreducible complex characters of alternating groups
@GeoffRobinson Given you're an active MO user, do you think this will fit there? I am doubting it.
comment Is $\text{Hom}(\prod_p \Bbb Z/p\Bbb Z, \Bbb Q) = 0$ possible without choice?
(Note the argument shows more generally that in ZFC any abelian group $G$ with an element of infinite order has ${\rm Hom}(G,\Bbb Q)\neq 0$)
comment Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
Bill, I think readability will improve for the uninitiated if you included some words in the proof that $h$ is onto. I think the kernel part is clearer. One can obtain the same result using normal forms -- see my answer.
revised Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
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comment Is $R$ PID if every submodule of a free $R$-module is free?
@RickyDemer Dominios de ideales principales. =)
comment Find up to isomorphism all the quotient groups of composition series of a group of order $30$.
@DerekHolt I think the OP is talking about the composition factors of a composition series. Perhaps the OP is asking the determine such composition factors.
answered Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
comment Rings in which every maximal ideal is a direct sum of cyclic modules
Please make your title more informative.
revised Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
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