Real Numbers - Gonit Sora

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Real Numbers

A collection of 3 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

Construction of Real Numbers Using Dedekind Cuts

Cauchy Sequences

Construction of Real Numbers Using Dedekind Cuts

We all know about rational numbers. Informally, these are ratios of integers, i.e., numbers of the form where and are integers (with of course). Any two rational numbers have a sum a product and there is an order relation such that or These operations and the relation obey certain

Jugendtraum of a Mathematician

Algebraic Numbers

Jugendtraum of a Mathematician

1. Kronecker’s Jugendtraum There is a phrase “Kronecker’s Jugendtraum (dream of youth)” in mathematics. Leopold Kronecker was a German mathematician who worked in the latter half of the 19th century. He obtained his degree at the University of Berlin in 1845 when he was 22 years old, and