Real Sequences

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function…

Smart Fallacies: i=1, 1= 2 and 1= 3

This mathematical fallacy is due to a simple assumption, that \$ -1=\dfrac{-1}{1}=\dfrac{1}{-1}\$ . Proceeding with \$ \dfrac{-1}{1}=\dfrac{1}{-1}\$ and…

Set Theory, Functions and Real Number System

Sets In mathematics, Set is a well defined collection of distinct objects. The theory of Set as a…

Getting Started with Measure Theory

Last year, I managed to successfully finish Metric Spaces, Basic Topology and other Analysis topics. Starting from the…

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…

The Area of a Disk

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

Triangle Inequality

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

Numbers – The Basic Introduction

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

Just another way to Multiply

Multiplication is probably the most important elementary operation in mathematics; even more important than usual addition. Every math-guy…

Everywhere Continuous Non-differentiable Function

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