# Gödel numbering

## Introduction

### Gödel numbering

Gödel numbering assigns a unique number to each formula.

To contruct this we first assign a natural number to each symbol.

This gives us a sequence:

$$\{x_1, x_2, x_3,...,x_n\}$$

We can assign a unique number to this by using the first $$n$$ prime numbers.

$$2^{x_1}3^{x_2}5^{x_3}...$$

This number can then be prime factored to recover the sequence, and therefore the formula.