# New post in Real-analysis

## 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

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

November 8th, 2020

July 2nd, 2020

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

February 1st, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

April 29th, 2020

## Condition for Implicit Function Theorem

September 30th, 2020

## Find infinite collection of open sets in $\Bbb R$ whose intersection is open and nonempty

September 26th, 2020

August 1st, 2022