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Introduction

When doing mathematics, we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. Going from rational numbers to reals is more complicated. The easiest way at the start is probably infinite decimals. Dedekind Cuts can be used to get a bit more fancy. A Dedekind cut is a partition of the rational numbers into two sets, A and B, such that all elements of A are less than all elements of B, and A contains no largest rational number. It corresponds to a point on the natural number line. A is all the rationales to the left, and B is all the rationales to the right, including the point if it is rational.

But little niggles remain.

Cracks In Mathematics

Everyone has probably seen why x = .9999999….. = 1. It’s simple. 10*.99999999999…. = 9.9999999…. 10*x – x = 9*x = 9 or x=1. Everything sweet. As an exercise, go to youtube, and you will see many videos on why it is true or not true. The reason the debate rages is...

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