New posts in real-analysis

Are rotations of $(0,1)$ by $n \arccos(\frac{1}{3})$ dense in the unit circle?

real-analysis geometry analysis

fonction inverse of $f(x)=\sqrt{x+2}+\sqrt{x}$

real-analysis calculus analysis inverse inverse-function

Convergence for $\sum_{k=1}^{\infty}(1-\cos(\frac{1}{\sqrt{k}}))$

real-analysis calculus sequences-and-series

seek a direct method to show $(a_k)\in l^2$

real-analysis analysis inequality soft-question

Rudin Theorem 3.27

Which is the better approximation to $e$?

real-analysis limits

Is this sequence Cauchy?

real-analysis uniform-convergence cauchy-sequences

How to show that $x^{1/n}$ is uniformly continuous

real-analysis continuity proof-explanation uniform-continuity

Irrationals in $[0,1]$ does not have measure zero

real-analysis measure-theory

Can $\mathbb{R}$ be written as an ascending union of proper additive subgroups?

real-analysis group-theory axiom-of-choice infinite-groups

What does countable union mean?

real-analysis self-learning

Computing in closed form $\sum_{n=1}^{\infty}\frac{\operatorname{Ci}\left(\frac{3}{4}\zeta(2) \space n\right)}{n^2}$

calculus real-analysis integration sequences-and-series

Regularity of the function $|x|^ax$

calculus real-analysis analysis limits functions

Distance is (uniformly) continuous

Convergence of $\int_0^\infty $sin$ (x^p) dx$

real-analysis integration convergence-divergence improper-integrals

If $\|\left(f'(x)\right)^{-1}\|\le 1 \Longrightarrow$ $f$ is an diffeomorphism

real-analysis algebraic-topology covering-spaces

Essential Supremum with the continuous function?

Calculating a limit of integral

calculus real-analysis limits

$\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test?

real-analysis sequences-and-series power-series

How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?

real-analysis calculus integration sequences-and-series definite-integrals