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Mar
27
awarded  Popular Question
Mar
13
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 . . .
Mar
9
answered Group Theory Lemma Proof
Mar
9
comment Does a Banach space always contain an element of arbitrarily large norm?
@N.S.: Touché :)
Mar
9
answered Does a Banach space always contain an element of arbitrarily large norm?
Mar
8
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".
Feb
23
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 $m>1$.
Feb
23
revised Is every real $\in(0,1)$ between the reciprocals of two consecutive integers?
added 184 characters in body
Feb
23
answered Is every real $\in(0,1)$ between the reciprocals of two consecutive integers?
Feb
12
comment Does interior of closure of open set equal the set?
Of course, the punctured disk. Thanks a lot, Brian. You are too awesome :)
Feb
12
comment Does interior of closure of open set equal the set?
Does there exist such counterexample with $A$ connected? It seems no, to me.
Feb
12
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).
Feb
12
comment Convergence in measure implies convergence almost everywhere (on a countable set!)
@Aubrey: No problem! Thanks for linking the new question.
Jan
30
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".
Jan
27
awarded  Nice Question
Jan
17
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
Jan
17
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 $x>0$?
Dec
30
comment An ideal that is radical but not prime.
@user26857, Konstantin Ardakov: Thanks a lot for the examples.
Dec
24
accepted Bounding $\sum_{p\leq x} \chi(p )$ for non-principal character $\chi$
Dec
23
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!