Introduction

Motivation

This series acts as a foundation for later series and posts that I want to make. Especially when you try to define things like exponential functions in real numbers. You really have to go back to the roots of what a real number is in order to derive anything. An unexpected result that I’ve learned from studying real analysis is that exponentiation is way more complicated than it seems

What Will I Cover

Build up the real numbers using the two standard methods: Cauchy Sequences and Dedekind Cuts. Start from the natural numbers with the peano axioms. Show the standard set-theory model. Build the integers and the rational numbers. Then build the real numbers. Then I’ll prove that the real numbers are complete.