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The video proves that there are infinitely many natural numbers by using a proof by contradiction. It assumes the opposite—that there is a finite amount of natural numbers—and then shows that this assumption leads to a logical contradiction.

Conditions: The proof method is proof by contradiction (PBC).; The set under discussion is $\mathbb{N}$, the natural numbers.; The arithmetic fact used is that adding 1 to a natural number yields a larger natural number.

The video proves that there are infinitely many natural numbers by using a proof by contradiction. It assumes the opposite—that there is a finite amount of natural numbers—and then shows that this assumption leads to a logical contradiction.

Conditions: The proof method is proof by contradiction (PBC).; The set under discussion is $\mathbb{N}$, the natural numbers.; The arithmetic fact used is that adding 1 to a natural number yields a larger natural number.