e - Gonit Sora

Gonit Sora

Sign in Subscribe

e

A collection of 2 posts

Construction of the system of real numbers by Cauchy sequences

Cauchy Sequences

Construction of the system of real numbers by Cauchy sequences

In a previous article, we explained the construction of real numbers using Dedekind Cuts; in this article we will explain the construction using Cauchy sequences. A sequence of rational numbers is a function from the set of positive integers into For a positive integer the image is generally denoted by

Napier's Constant "e" is Transcendental

Napier's Constant "e" is Transcendental

This theorem was first proved by Hermite in 1873. The below proof is near the one given by Hurwitz. We at first derive a couple of auxiliary results. Let $$f(x)$$ be any polynomial of degree $$ mu$$ and $$ F(x)$$ the sum of its derivatives, $$displaystyle F(x) := f(x)