Abhishek Parab
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 Jun 27 comment The regular semisimple element in the algebraic group If $K$ in the question is algebraically closed then any semisimple element $s$ can be diagonalized; it is regular if and only if all eigenvalues are distinct. This is equivalent, as Turgeon refers to Borel's book, to being outside the kernel of every root. Jun 12 comment Need a hint to evaluate $\lim_{x \to 0} {\sin(x)+\sin(3x)+\sin(5x) \over \tan(2x)+\tan(4x)+\tan(6x)}$ The limit in your question can be evaluated by dividing the numerator and denominator by $x$ and then evaluating each separately. Apr 10 accepted Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? Dec 23 awarded Caucus Oct 9 comment On Rieman integral Taking square roots is a well-defined continuous (hence integrable) function. Jun 6 revised A variation of Kuratowski closure-complement problem using dual cones OP changed the question. May 28 suggested rejected edit on A variation of Kuratowski closure-complement problem using dual cones May 28 answered A variation of Kuratowski closure-complement problem using dual cones Dec 23 awarded Yearling Feb 23 comment On the ring of integers of a compositum of number fields Dear Bruno, can this solution be modified to find the ring of integers in case that none of $m$ and $n$ are 1 mod 4? Feb 23 comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? Bruno, thanks; this seems a useful result to keep handy. Feb 23 comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? Too bad if so.. :( Feb 23 comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? Qiaochu, I have edited the question. Feb 23 revised Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? added 4 characters in body Feb 23 asked Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$? Aug 12 comment Find an ideal $I$ of $\mathbb{Z}[i]$ such that $\mathbb{Z}[i]/{I}$ is a field What is R in the question? Aug 12 answered Find an ideal $I$ of $\mathbb{Z}[i]$ such that $\mathbb{Z}[i]/{I}$ is a field Jun 13 comment Let $X = \Bbb{R}$ with the discrete metric. Is $X$ connected? @BrandonCarter There are stories of Emil Artin hurling a chalk or duster towards a student who'd ask What about the empty set?" Jun 12 comment Is the sum and difference of two irrationals always irrational? $\sqrt 2 - 1$ is irrational being the sum of a rational and an irrational. Jun 12 comment Let $X = \Bbb{R}$ with the discrete metric. Is $X$ connected? No discrete topology can ever be connected. You answer your own question. What do you mean by "formal way"?