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### Questions (89)

 7 Find all real polynomials $p(x)$ that satisfy $\sin( p(x) ) = p( \sin(x) )$ 6 If $\Sigma \vdash \phi$ implies $\Sigma \vdash \varphi$ then $\Sigma \vdash \phi \to \varphi$ on propositional logic? 5 Prove that for a polynomial function $f$ if $f(x) \geq 0$ for all $x$, then $f(x) + f'(x) + \cdots + f^{(n)} (x) \geq 0$ [duplicate] 5 Can I derive $i^2 \neq 1$ from a presentation $\langle i, j \mid i^4 = j^4 = 1, ij = j^3 i\rangle$ of Quaternion group $Q$? 5 (Dummit's AA, 1.5, P3) Are these presentations of the Quarternion group equivalent?

### Reputation (974)

 +5 How many distinct subgroups does the symmetric group $S_3$ have? +10 differentiable structure on mobius strip +5 Does every LCS has a convex balanced local base? +5 How to prove real symmetric matrix is diagonalizable (with reference request)

 4 Question on limit: $\lim_{x\to 0}\large \frac{\sin^2{x^{2}}}{x^{2}}$ 3 A question on transposes of matrices in muliplication and determinant 2 Does there exist $f:(0,\infty)\to(0,\infty)$ such that $f'=f^{-1}$? 0 Cardinality of a countably infinite set, once partitioned 0 For $t\in [ 0, 1 )$ is $\frac{xe^{tx}}{e^{x}-1}$ integrable over $x\in (0 , \infty )$?

### Tags (56)

 4 calculus × 10 0 abstract-algebra × 18 4 limits 0 real-analysis × 18 3 linear-algebra × 6 0 measure-theory × 12 3 matrices × 2 0 complex-analysis × 9 2 analysis × 8 0 ring-theory × 7

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