Category Archives: Proof

How to think about the proof (anbn)->(a,b) when

Posted on June 24, 2024 by Sumant Sumant

This is one of the standard proof in introductory analysis course about why the product of a converging sequence is a converging sequence. Here I am distilling how to think about the proof when you see the first time.

Posted in Proof, Real Analysis | Tagged | Leave a comment

Proof of Cauchy’s Integral theorem

Posted on March 29, 2024 by Sumant Sumant
Posted in Complex Analysis, Proof | Tagged | Leave a comment

Deriving Cauchy Riemann Equations

Posted on March 29, 2024 by Sumant Sumant
Posted in Complex Analysis, Complex Numbers, Proof | Tagged | Leave a comment

Prove for every natural number x there exists another natural number y such that x/y is not a natural number

Posted on February 2, 2024 by Sumant Sumant
Posted in Number Theory, Proof | Tagged | Leave a comment

Why we have even number of odd Vertices?

Posted on January 28, 2024 by Sumant Sumant
Posted in Graph Theory, Proof | Tagged , | Leave a comment

Proving the relation R on the set of ordered pairs ((a,b),(c,d)) whenever a+d=b+c is equivalence

Posted on December 9, 2023 by Sumant Sumant
Posted in Logic, Proof, Set Theory | Tagged | Leave a comment

Real Analysis: Proof why (anbn) converges to ab if (an) converges to a and (bn) converges to b

Posted on October 19, 2023 by Sumant Sumant
Posted in Proof, Real Analysis | Tagged | Leave a comment

IB HL (2n)! >= 2^n(n!)^2 (Mathematical Induction)

Posted on October 13, 2023 by Sumant Sumant

Use mathematical induction to prove that , for n

Posted in Mathematical Induction, Proof | Tagged , | Leave a comment

Proof: No Integral roots for a quadratic trinomial with all odd coefficients

Posted on September 25, 2023 by Sumant Sumant
Posted in Proof, Proof by Cases, Proof by Contradiction | Tagged , | Leave a comment

Even number of outside doors

Posted on August 28, 2023 by Sumant Sumant
Posted in Combinatorics, Graph Theory, Parity, Proof, Proof by Construction | Tagged , , , | Leave a comment