A brief introduction to p-adic numbers

TL;DR

This paper provides a concise overview of p-adic numbers, highlighting their basic properties, arithmetic operations, and norms from a classical analysis perspective.

Contribution

It offers a clear, introductory survey of p-adic numbers focusing on their fundamental features and similarities to real and complex numbers.

Findings

P-adic numbers have well-defined arithmetic operations.

They possess a norm similar to real and complex numbers.

The paper clarifies foundational aspects of p-adic number theory.

Abstract

In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex numbers.