Things seem more natural after sleep. I refer to math constructions like “Let’s build,” “Suppose we have,” and other proposals. Happily proceeding from definition to definition, and then to proofs, is the wall to climb. Thinking about math before doing a pullup: yes, let’s have an ordinal system and here are its properties.

Thinking in layers, we go from elements organized into groups discretized into classes, and each class representing some number of elements symbolized by digits, and these are called cardinal numbers, but the numerals themselves are actually natural numbers. And the endless list you built before is yet another layer; on top is the ordinal system.

This has the property of “before” and “after,” “precedes” and “follows.” On top of this (again) we have assemblages of men, a few of whom could have coincident heights – prohibited in the two levels beneath – an imposition of ranking that we had to explicitly define as possible before.