A Frivolous Theorem of the Natural Numbers

January, 2018


Alright, check this out. I think this is pretty funny.

Theorem: Almost every natural number is really, really big.

Proof: Suppose we take some number $n \in \mathbb{N}$ to be a threshold of "really, really big" such that if we add any number $k \in \mathbb{N}$ to $n$, the number $n+k$ is also "really, really big" and if we subtract any number $m \in \mathbb{N}$ from $n$, the number $n-m$ is not "really, really big". Then, since the naturals are bounded from below and unbounded from above, we have finitely many numbers below $n$ and infinitely many numbers above $n$. Thus, all but finitely many natural numbers are "really, really big".

$\blacksquare$