Frivolous Theorem of Arithmetic

chuckle lIt's actually not as frivolous as it looks, especially if you think about it in reverse, in the light of Kolmogorov Complexity. The fact that there are way, way fewer small integers has many pleasant implications.

E.g. for anything that can be put into a 1-to-1 correspondence with integers--things like computer programs, scientific hypothesis, etc, you can prove that "smaller" instances (in the sense of being mapped to smaller integers) have better chance of being bug-free, or more predictive of future observations, etc etc.

Bigger programs are composed of smaller programs, so the smaller a program is, the more likely it is to be included in, say, a standard library for that language, and the more likely it is to occur in programs written in that language.