New posts in real-analysis

Is this "reverse the limit" process right?

real-analysis limits

Challenging problem: Find $a$ where $\int_0^\infty \frac{\cos(ax)\ln(1+x^2)}{\sqrt{1+x^2}}dx=0$.

real-analysis calculus integration improper-integrals

Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set

real-analysis baire-category

Example of not being a sigma algebra as complement property does not hold

real-analysis measure-theory

Integrate product of Dirac delta and discontinuous function?

calculus real-analysis analysis

Outer Measure of the complement of a Vitali Set in [0,1] equal to 1

real-analysis measure-theory

If $f$ is a positive, monotone decreasing function, prove that $\int_0^1xf(x)^2dx \int_0^1f(x)dx\le \int_0^1f(x)^2dx \int_0^1xf(x)dx$

calculus real-analysis integration inequality

How to calculate $\lim_{x\to 0}\Big({1+\tan x \over 1+\sin x}\Big)^{1\over \sin x}$

real-analysis limits limits-without-lhopital

Convergence of the series $\sum a^{\sum \frac{1}{n}}$ [duplicate]

real-analysis sequences-and-series convergence-divergence

What's the component interval?

Principles of Mathematical Analysis, Dedekind Cuts, Multiplicative Inverse

real-analysis elementary-set-theory

Continuous function $f:\mathbb{R} \to \mathbb{R}$ such that $f^{-1}(\{y\})$ has two elements. [duplicate]

calculus real-analysis

Evaluate the general infinite square root [duplicate]

calculus real-analysis analysis derivatives proof-writing

If $f(A)\to A^{-1}$, prove that $f$ is continuous.

real-analysis continuity matrix-calculus

Prove that an increasing and surjective function is continuous.

real-analysis continuity

Can we find uncountably many disjoint dense measurable uncountable subsets of $[0,1]$?

real-analysis lebesgue-measure

Does there exist a continuous onto function from $\mathbb{R}-\mathbb{Q}$ to $\mathbb{Q}$?

Limit of the nth power of certain partial sums

calculus real-analysis limits

In general, why is the product topology not equal to the box topology

real-analysis general-topology product-space

Let the sequence $\{a_n\}$ be defined as $a_1=1$ and $a_{n+1} = \frac{6a_n+3}{a_n+4}$. Show that $a_n \lt 3$ and the sequence is increasing.

real-analysis sequences-and-series cauchy-sequences