# There are infinitely many natural numbers

By contradiction, suppose there is a finite amount of natural numbers.

Take the greatest natural number and call it $n$.

Now consider $n + 1$. There are two facts about $n + 1$:

1. $n + 1$ is greater than $n$
2. Since $n \in \N$, then $n + 1 \in \N$

This is in contradiction with the statement earlier that there exists a largest natural number.

Hereby it is proven that there are infinitely many natural numbers.