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 29 Hard combinatorics and probability question. 16 Is there a set non-countable around zero but countable elsewhere? 14 Evaluating $\lim_{n \to +\infty}\frac{1}{n}\left({\frac{n}{n+1} + \frac{n}{n+2} + \cdots + \frac{n}{2n}}\right)$ 11 Prove that ${ a }^{ 2 }+2ab+{ b }^{ 2}\ge 0$ without using $(a+b) ^{ 2 }$ 10 find the value of $f'(5)$ for given function

### Reputation (13,094)

 +10 Random directions on hemisphere oriented by an arbitrary vector +10 Why square a constant when determining variance of a random variable? +10 Hard combinatorics and probability question. +10 Show that the counting measure has no Lebesgue decomposition.

### Questions (7)

 5 Continuum hypothesis : Number of connected components of $A^c$ in $\Bbb R$ 3 Does it always exist an infinite subset of sequences that satisfy this property? 3 Proof that a sequence of set has a set dense somewhere in $[a,b]$ 2 Existence of an uncountable set of sequence 1 Does it exist a countable set such that any sequence with value in $\mathbb{N}$ is bounded by a sequence in this set?

### Tags (237)

 223 real-analysis × 123 78 integration × 39 172 calculus × 69 71 general-topology × 29 83 analysis × 43 65 probability × 24 81 sequences-and-series × 41 63 linear-algebra × 32 79 functional-analysis × 55 47 functions × 24

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 Mathematics 13,094 rep 1229 Stack Overflow 218 rep 28 Worldbuilding 141 rep 4 Politics 121 rep 2 Game Development 111 rep 2

 Yearling × 4 Pundit Revival Curious Enlightened × 4 Good Answer Nice Answer × 6 Disciplined Generalist Peer Pressure

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