Abstract:
In this talk, I will construct the field of p-Adic numbers $\mathbb{Q}_p$ for a prime $p$ as a completion of the rational numbers $\mathbb{Q}$ with respect to the p-adic norm. This is a non-Archimedean norm, which has some interesting consequences for the topology of the resulting field, including that every point of a ball is its center. We'll also talk about the algebraic properties of the p-adic integers $\mathbb{Z}_p$ and do an example of an integral if time permits. This talk should be accessible to undergraduates.