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 70 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? 16 An inequality $\,\, (1+1/n)^n<3-1/n \,$using mathematical induction

### Reputation (11,511)

 +25 If complex no. ($z$) satisfying $\frac{1}{2}\leq |z|\leq 4\;,$ Then Max. and Min. of $\left|z+\frac{1}{z}\right|$ +10 $\omega_1$-closedness and fullness for $\searrow$ $\omega$-sequences +10 An inequality $\,\, (1+1/n)^n<3-1/n \,$using mathematical induction +10 Theorem 3.29 in Baby Rudin

### Questions (49)

 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? 12 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 (133)

 157 real-analysis × 59 53 elementary-set-theory × 32 115 calculus × 35 53 elementary-number-theory × 13 106 sequences-and-series × 25 51 abstract-algebra × 20 70 arithmetic 51 analysis × 15 65 general-topology × 36 46 limits × 19

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