# sqrt2.tex -...

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\documentclass[12pt]{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage[letterpaper, margin=1 in]{geometry} \usepackage{graphicx} \usepackage{hyperref} \usepackage{plain} \usepackage{amsrefs} \title{The Irrationality of $\sqrt{2}$} \author{Paul Glaze} \date{\today} \begin{document} \maketitle %\section{Introduction}\label{firstsection} % % % %There are many different representations of numbers in mathematics. Few are as important as irrational numbers. Calling them irrational numbers is probably the second worst name for a numbering system, next to imaginary. Irrational numbers are somewhat counter intuitive at times because they can not be represented as a fraction. Irrational number have been around for a very long time it was a Pythagorean named Hippasus who first proved them \cite{Wikipedia}. It has been said that people reacted quite violently to his assertion of a numbers. But thanks to this proof it opened the door to many advancements in mathematics. Before for this point number were thought to be integers or ratios of integers. % %In the first part of the paper we ill discuss how Hippasus came across irrational numbers \cite{Fritz}. At the same time why irrational numbers are needed, particularly because they are impassible to represent as a ratio if only using integers. They do not terminate when represented as a decimal. In the next section of he paper we will expand on the use of irrational numbers and how they have been used to prove other mathematical structures. This paper will finished by showing that the $\sqrt{2}$ is no more irrational than any other number \cite{Agafonov}. It is just miss understood.

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