# cactuar

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bio website reddit.com/r/… location meatspace age member for 2 years, 8 months seen Nov 12 at 20:29 profile views 1,109

when someone smiles at me, all I see is an ape bearing its teethe

# 592 Actions

 Aug2 accepted If $N$ is a normal subgroup of $G$ with $N$ and $G/N$ solvable, prove that $G$ is solvable Aug2 asked If $N$ is a normal subgroup of $G$ with $N$ and $G/N$ solvable, prove that $G$ is solvable Jul27 comment Proving $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$, given that $\theta^3 + 11\theta - 4 = 0$ Thank you for the help Robert. However I would like to check my understanding: The reason its min poly couldn't be a quartic or higher is because $[\mathbb{Q}(\theta):\mathbb{Q}]=3$, and since $\theta$ and $\frac{\theta^2 -\theta}{2}$ can each be constructed from the other in $\mathbb{Q}(\theta)$, this means it couldn't be quadratic or lower. Thus its min poly had to be a cubic. Thanks. Jul27 accepted Proving $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$, given that $\theta^3 + 11\theta - 4 = 0$ Jul27 comment Proving $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$, given that $\theta^3 + 11\theta - 4 = 0$ Thanks for the elaboration. Jul27 asked Proving $\frac{-\theta + \theta^2}{2}$ is an algebraic integer in $K = \mathbb{Q}(\theta)$, given that $\theta^3 + 11\theta - 4 = 0$ Jul25 accepted How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer Jul25 comment How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer I see that it does lie in said splitting field, but could you explain more what you mean by the rest of your comment? Jul25 revised How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer added 82 characters in body Jul25 asked How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer Jul23 accepted My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$ Jul22 accepted Strange application of Cauchy's Integral Theorem Jul22 comment Strange application of Cauchy's Integral Theorem Ohhh I see it! Thank you for this. Jul22 asked Strange application of Cauchy's Integral Theorem Jul19 comment My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$ thankssssssssss Jul19 comment My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$ Ohhh gosh ok that clears things up, thanks. Jul19 asked My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$ Jul17 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Yes but in this case we are ok right? Jul16 answered Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Jul16 comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Ok so past some point $x_0$ or within some neighborhood of a point, that makes sense; thanks! I think I'm going to spend some time proving those identities you listed to help my understanding.