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 68 which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$ 34 The series $\sum_{n=1}^{+\infty}\frac{1}{1^2+2^2+\cdots+n^2}.$ 30 Does $\bigcap_{n=1}^{+\infty}(-\frac{1}{n},\frac{1}{n}) = \varnothing$? 18 Does the sequence $1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,1,1,-1,\ldots$ have a closed form? 14 An inequality $\,\, (1+1/n)^n<3-1/n \,$using mathematical induction

### Reputation (10,939)

 +5 Finite complement topology over $\Bbb{R}$ is not second-countable under ZF? +5 Integration of $\sqrt{x+\sqrt{x^2+3x}}$ +35 Write an inductive proof that if there is a surjection $f : \lceil m \rceil → \lceil n \rceil$ then $m ≥ n$. +15 Why is $S = \{ x \in \mathbb{Q} | 2 < x^2 < 3 \}$ closed in $\mathbb{Q}$?

### Questions (42)

 14 Can we prove the existence of $A\cup B$ without the union axiom? 13 If polynomial with rational number is injective on rationals then it is injective on reals? 9 Integration of $\sqrt{x+\sqrt{x^2+3x}}$ 9 The cardinality of the set of all linear order types over $\omega$ is $2^{\aleph_0}+\aleph_1$ in ZF+AD? 7 There is a second-order sentence that is valid in standard semantics but not valid in Henkin semantics?

### Tags (127)

 153 real-analysis × 58 53 elementary-set-theory × 32 112 calculus × 34 53 elementary-number-theory × 13 104 sequences-and-series × 23 52 abstract-algebra × 21 68 arithmetic 50 analysis × 15 64 general-topology × 36 43 limits × 18

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