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Real-analysis
New post in Real-analysis
Understanding the proof that the series $\sum \frac{1}{n^2}$ is convergent
August 21st, 2022
proof-explanation
real-analysis
Revisit "Prove that the inverse image of an open set is open"
January 17th, 2023
general-topology
continuity
real-analysis
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
real-analysis
lebesgue-measure
measure-theory
lebesgue-integral
The composition of continuous functions on $\mathbb{R}$ is continuous
January 3rd, 2023
real-analysis
hard problem in sequences
December 11th, 2022
sequences-and-series
real-analysis
Local and Global Invertibility
August 18th, 2022
real-analysis
derivatives
inverse
jacobian
Show that $f(x)=3x^{2}-2x+1$ is continuous at 2
August 16th, 2022
proof-verification
continuity
real-analysis
The discrete metric on $\mathbb R $ is not induced by a norm
December 5th, 2022
real-analysis
Does countably infinite number of zeros add to zero?
July 23rd, 2022
real-analysis
Consider the following map:
October 24th, 2022
real-analysis
functional-analysis
complex-analysis
inductive set and examples
July 22nd, 2022
real-analysis
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
abstract-algebra
general-topology
measure-theory
lebesgue-measure
real-analysis
Is the sequence $\{1/n^2\}$ Cauchy?
August 1st, 2022
real-analysis
sequences-and-series
cauchy-sequences
Supremum and infimum of $\frac{x}{\sin x}$ on $\left[0,\frac{\pi}{2}\right]$
November 12th, 2020
supremum-and-infimum
real-analysis
Find a seven digit number which describes itself
August 1st, 2022
real-analysis
calculus
algebra-precalculus
problem-solving
puzzle
Functions and trig question, finding minimum value
August 1st, 2022
algebra-precalculus
real-analysis
Proof of the intersection of boundary of a set and a connected set is nonempty
December 15th, 2020
real-analysis
Show that $\arctan(x)$ exists and is differentiable in $(-\pi/2, \pi/2)$
August 1st, 2022
calculus
real-analysis
Baby Rudin Chapter 4 Exercise Questions 5 and 6
August 1st, 2022
real-analysis
self-learning
The supremum and infimum of the sequence $\{(-1)^n/n^2\}$.
November 20th, 2020
supremum-and-infimum
real-analysis
Examples where Rolle's Theorem fails for following
August 1st, 2022
calculus
real-analysis
$\sin(1/x)$ is not BV.
April 28th, 2020
real-analysis
bounded-variation
Real Analysis: Prove every unbounded sequence contains a divergent monotone subsequence
December 15th, 2020
sequences-and-series
real-analysis
If f and g are uniformly continuous then fg is uniformly continuous
November 8th, 2020
real-analysis
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
calculus
real-analysis
integration
gamma-function
Examples of a strongly continuous function and a weakly continuous function.
August 1st, 2022
real-analysis
Proving that the integrals of two functions are the same if they are equal everywhere except a point
August 1st, 2022
calculus
integrable-systems
integration
real-analysis
Proving Riemann Sums via Analysis
July 2nd, 2020
integration
riemann-sum
proof-writing
real-analysis
Continuous function: $ Z=${$x \in \mathbb{R} : f(x) = 0$} is closed
November 8th, 2020
general-topology
real-analysis
Double sequence, two sequences converge, but to different limits?
February 1st, 2020
convergence-divergence
real-analysis
examples-counterexamples
calculus
sequences-and-series
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