# cactuar

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bio website reddit.com/r/… location meatspace age member for 2 years, 9 months seen Dec 4 at 3:52 profile views 1,115

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

# 112 Questions

 9 Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$ 8 What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$ 7 What property of a matrix causes $\|e^{tA}\|_2$ to oscillate as $t\rightarrow\infty$? 7 Show bounded harmonic function on $\mathbb{C}$ is constant. 7 For $I,J$ ideals, show that $IJ\subseteq (I\cap J)(I+J)$

# 1,690 Reputation

 +5 For $I,J$ ideals, show that $IJ\subseteq (I\cap J)(I+J)$ +5 Prove that $\displaystyle\prod_{q\in \mathbb{Q}^{\times}}|q|=1$ +5 Question about The Weierstrass Factorization Theorem +5 Given that $(X_n)_{n\geq 0}$ is a Markov Chain, prove that $(X_{kn})_{n\geq 0}$ is a Markov Chain

 4 Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$ 3 Accidents of small $n$ 2 Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$ 1 Complex Analytic Proof of the Gaussian Integral $\int_{-\infty}^{\infty}e^{-z^2}dz=\sqrt{\pi}$ 0 Showing that $f(x)=x\sin (1/x)$ is not absolutely continuous on $[0,1]$

# 85 Tags

 4 abstract-algebra × 18 1 residue-calculus × 3 4 commutative-algebra × 3 0 real-analysis × 15 3 complex-analysis × 28 0 measure-theory × 12 3 examples-counterexamples × 2 0 probability × 9 3 big-list 0 number-theory × 7

# 14 Accounts

 Mathematics 1,690 rep 417 Academia 301 rep 27 Code Review 206 rep 7 Cross Validated 197 rep 9 Stack Overflow 192 rep 8