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

Does countably infinite number of zeros add to zero?

July 23rd, 2022

Consider the following map:

October 24th, 2022

inductive set and examples

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

Is the sequence $\{1/n^2\}$ Cauchy?

August 1st, 2022

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

November 12th, 2020

Find a seven digit number which describes itself

August 1st, 2022

Functions and trig question, finding minimum value

August 1st, 2022

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

December 15th, 2020

Show that $\arctan(x)$ exists and is differentiable in $(-\pi/2, \pi/2)$

August 1st, 2022

Baby Rudin Chapter 4 Exercise Questions 5 and 6

August 1st, 2022

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

November 20th, 2020

Examples where Rolle's Theorem fails for following

August 1st, 2022

$\sin(1/x)$ is not BV.

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

Prove that $\int_0^\infty e^{-x^4}\ dx = \Gamma\left(\frac{5}{4}\right) = \left(\frac{1}{4}\right)!$ using the gamma function

May 9th, 2020

Examples of a strongly continuous function and a weakly continuous function.

August 1st, 2022

Proving that the integrals of two functions are the same if they are equal everywhere except a point

August 1st, 2022

Proving Riemann Sums via Analysis

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