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# 670 Questions

 32 To show that the set point distant by 1 of a compact set has Lebesgue measure $0$ 20 Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ 16 There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent. 14 How to show path-connectedness of $GL(n,\mathbb{C})$ 14 I need to calculate $x^{50}$ [duplicate]

# 12,532 Reputation

 +5 I need to calculate $x^{50}$ -2 we need to show $y\equiv 0$ +5 fixed point of homeomorphism and compactness of a complete metric space. -2 identify quotient group

 30 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ 12 $AB-BA=I$ having no solutions 9 If $2^x=3^y=6^{-z}$ then prove that:$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ 7 Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$? 6 Let $f$ be an analytic function such that if $|z|=\frac{1}{2}$ then $f(z)\in \mathbb{R}$. Prove that $f$ is constant.

# 154 Tags

 90 real-analysis × 201 34 integration × 11 74 calculus × 40 33 linear-algebra × 137 57 general-topology × 124 33 group-theory × 51 55 complex-analysis × 155 30 indefinite-integrals × 2 35 trigonometry × 6 26 limits × 22

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