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 20 $\infty - \infty = 0$ ? 19 Given real numbers: define integers? 12 Is $X_n = 1+\frac12+\frac{1}{2^2}+\cdots+\frac{1}{2^n}; \forall n \ge 0$ bounded? 11 Infinite series $\sum_{n=0}^\infty \frac{(-3)^n}{n!}$ 10 Solving $xe^{-x}+2e^{-x}=0$

### Reputation (9,060)

 +20 How can I prove $2\sin x+\tan x \geq 3x$? +10 Can a limit of an integral be moved inside the integral? +10 Archimedean Property and Real Numbers +10 Moving a limit inside an infinite sum

### Questions (17)

 19 Book on the Rigorous Foundations of Mathematics- Logic and Set Theory 12 Proof that a function with a countable set of discontinuities is Riemann integrable without the notion of measure 5 Non elementary antiderivative of $\phi(\cos x,\sin x)$ when $\phi(x,y)$ is a rational real function? 4 Principles of Mathematical Analysis, Dedekind Cuts, Multiplicative Inverse 3 Proof using Darboux's Definition: $\int_0^1f=\lim_{n\to \infty}\frac1n\sum_{i=1}^{n}f\left(\frac in\right)$

### Tags (86)

 234 calculus × 77 64 proof-writing × 10 164 real-analysis × 80 49 continuity × 16 117 limits × 45 48 analysis × 28 107 integration × 41 47 algebra-precalculus × 12 105 sequences-and-series × 32 43 functions × 13

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