This talk on $p$-adic Numbers was held on Friday February 3, 2017 in MC 4045. The talk was given by Akshay Tiwary.

## Abstract

In this talk we will discover an alternate way to define the "size" of a ration al number. We will define the p-adic absolute value and see that this absolute value is Non-archimedean and that this fact leads to a a geometry that is very different from the geometry of the Real numbers (every p-adic triangle is isosc eles!). In addition I will show you some fun ideas from p-adic numbers (which I will denote by $\mathbb{Q}_p$ like the fact that $\sum_{n = 1}^{\infty} 3^n$ converges and how every element of $\mathbb{Q}_p$ has a base $p$ expansion. This is meant to be a very leisurely talk with almost no prerequisites and it should be fun so please come for it!