50 Can every integer greater than 5 be written as the sum of exactly one prime and one composite? 17 If every real-valued continuous function is bounded on $X$ (metric space), then $X$ is compact. 12 Step Function and Simple Functions 9 If $f(x+1)+f(x-1)=\sqrt 3 f(x), \forall x$ then $f$ is periodic. 9 Does There Exist an Injective Continuous Map $f:\mathbf R^3\to \mathbf R^2$.

### Reputation (7,924)

 +10 Step Function and Simple Functions +10 Limit of consecutive Lp norms +10 What is the difference between a Hamel basis and a Schauder basis? +10 Completeness of Measure spaces

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### Tags (135)

 127 real-analysis × 66 50 arithmetic 81 calculus × 41 49 sequences-and-series × 21 68 measure-theory × 31 43 limits × 17 56 prime-numbers × 2 41 integration × 25 52 functional-analysis × 32 30 general-topology × 10

### Bookmarks (49)

 64 Does the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}}$ converge or diverge? 63 Is $\sum\limits_{n=1}^\infty \frac{|\sin n|^n}n$ convergent？ 54 Does $|n^2 \cos n|$ diverge to $+\infty$? 49 Prove/disprove $(\int_0^{2 \pi} \!\!\cos f(x) \, d x)^2+(\int_0^{2 \pi}\!\!\! \sqrt{(f'(x))^2+\sin ^2 f(x)} \, dx)^2\ge 4\pi^2$ 34 Convergence of a series with repeated sines