Prism
Reputation
3,788
Next privilege 5,000 Rep.
Approve tag wiki edits
 Mar27 awarded Popular Question Mar13 comment Prove the fractional field $Q(\mathbb{R})$ of the integral domain $\Bbb R$ is $\mathbb{R}$. The fraction field of an integral domain $R$ is the smallest field containing $R$ (in an appropriate sense). But if $R$ is already a field . . . Mar9 answered Group Theory Lemma Proof Mar9 comment Does a Banach space always contain an element of arbitrarily large norm? @N.S.: Touché :) Mar9 answered Does a Banach space always contain an element of arbitrarily large norm? Mar8 comment If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian. I am pretty sure this problem also appears in Herstein's classic "Topics in Algebra". Feb23 comment Is every real $\in(0,1)$ between the reciprocals of two consecutive integers? @user7530: Good point. Since $\alpha<1$ and $m\in S$, we know that $m>m\alpha\geq 1$, so $m>1$. Feb23 revised Is every real $\in(0,1)$ between the reciprocals of two consecutive integers? added 184 characters in body Feb23 answered Is every real $\in(0,1)$ between the reciprocals of two consecutive integers? Feb12 comment Does interior of closure of open set equal the set? Of course, the punctured disk. Thanks a lot, Brian. You are too awesome :) Feb12 comment Does interior of closure of open set equal the set? Does there exist such counterexample with $A$ connected? It seems no, to me. Feb12 comment Convergence in measure implies convergence almost everywhere (on a countable set!) Explained here (just adding this so Davide sees it, in case he hasn't). Feb12 comment Convergence in measure implies convergence almost everywhere (on a countable set!) @Aubrey: No problem! Thanks for linking the new question. Jan30 comment How does $n(n-1)(n-2)\cdots(n-m+1) \cdot \frac{(n-m)(n-m-1)\cdots1}{(n-m)(n-m-1)\cdots1} = \frac{n(n-1)(n-2)\cdots1}{(n-m)(n-m-1)\cdots1}$ @user1766555: Right click on the formula --> "Show Math as" --> "TeX Commands". Jan27 awarded Nice Question Jan17 comment can a number of the form $x^2 + 1$ be a square number? Yes, now your comment has made it much more clear. Thank you. +1 Jan17 comment can a number of the form $x^2 + 1$ be a square number? I understand all the other answers, but not this one. Since it has gotten 22 upvotes, I am sure I am missing something. Can someone elaborate how this argument shows $x^2+1$ is not a perfect square for $x>0$? Dec30 comment An ideal that is radical but not prime. @user26857, Konstantin Ardakov: Thanks a lot for the examples. Dec24 accepted Bounding $\sum_{p\leq x} \chi(p )$ for non-principal character $\chi$ Dec23 comment Let $\{a_n\}_{n=1}^\infty$ be an infinite sequence. Does there exist an infinite series whose partial sums is $\{a_n\}_{n=1}^\infty$? "Does there exist…" part is about existence of the series whose partial sums is $\{a_n\}$. Let's look at the beginning of the question. It says "Let $\{a_n\}_{n=1}^{\infty}$ be an infinite sequence of real numbers…" It is an arbitrary sequence of real numbers!