## Irrational Numbers and The Proofs of their Irrationality

“Irrational numbers are those real numbers which are not rational numbers!” Def.1: Rational Number A rational number is…

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11 posts

- byGaurav Tiwari
- October 1, 2014

- byGaurav Tiwari
- January 8, 2018

If you are aware of elementary facts of geometry, then you might know that the area of a…

- byGaurav Tiwari
- March 28, 2015

Triangle inequality has its name on a geometrical fact that the length of one side of a triangle…

- byGaurav Tiwari
- December 21, 2017

Ramanujan (1887-1920) discovered some formulas on algebraic nested radicals. This article is based on one of those formulas.…

- byGaurav Tiwari
- April 5, 2014

If mathematics was a language, logic was the grammar, numbers should have been the alphabet. There are many…

- byGaurav Tiwari
- January 30, 2018

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of…

- byGaurav Tiwari
- December 17, 2016

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails…

- byGaurav Tiwari
- November 19, 2013

Statement A series $ \sum {u_n}$ of positive terms is convergent if from and after some fixed term…

- byGaurav Tiwari
- March 17, 2019

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem $ \int \int \int_{V} x^{l-1} y^{m-1} z^{n-1} dx dy…

- byGaurav Tiwari
- April 1, 2015

We all know that the derivative of $x^2$ is 2x. But what if someone proves it to be just x?

- byGaurav Tiwari
- December 21, 2017

Consider a sequence of functions as follows:- $ f_1 (x) = \sqrt {1+\sqrt {x} } $ $ f_2…

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