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.