# New post in Real-analysis

## Understanding the proof that the series $\sum \frac{1}{n^2}$ is convergent

August 21st, 2022

## Revisit "Prove that the inverse image of an open set is open"

January 17th, 2023

## Let $f:[0,1] \to \mathbb{R}$ be given by $f(x)=0$ if $x$ rational and if $x$ is irrational , then $f(x)=9^n$

January 4th, 2023

## The composition of continuous functions on $\mathbb{R}$ is continuous

January 3rd, 2023

## hard problem in sequences

December 11th, 2022

## Local and Global Invertibility

August 18th, 2022

## Show that $f(x)=3x^{2}-2x+1$ is continuous at 2

August 16th, 2022

## The discrete metric on $\mathbb R$ is not induced by a norm

December 5th, 2022

July 23rd, 2022

## Consider the following map:

October 24th, 2022

July 22nd, 2022

## the $\sigma$ algeba generated by the class of open intervals with rational end points coincide with the borel $\sigma$ algebra on the real line.

September 29th, 2022

August 1st, 2022

## Supremum and infimum of $\frac{x}{\sin x}$ on $\left[0,\frac{\pi}{2}\right]$

November 12th, 2020

August 1st, 2022

August 1st, 2022

## Proof of the intersection of boundary of a set and a connected set is nonempty

December 15th, 2020

August 1st, 2022

August 1st, 2022

## The supremum and infimum of the sequence $\{(-1)^n/n^2\}$.

November 20th, 2020

August 1st, 2022

April 28th, 2020

## Real Analysis: Prove every unbounded sequence contains a divergent monotone subsequence

December 15th, 2020

## If f and g are uniformly continuous then fg is uniformly continuous

November 8th, 2020

May 9th, 2020

August 1st, 2022

August 1st, 2022

July 2nd, 2020

## Continuous function: $Z=${$x \in \mathbb{R} : f(x) = 0$} is closed

November 8th, 2020

## Double sequence, two sequences converge, but to different limits?

February 1st, 2020