Generator

ordinal

A generator in the logic library, called 8 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

ordinal is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

Order types drawn on the line: ω, ω+1, ω·2, ω²Number lines with tick marks accumulating at limit points, one line per order type.ωω+1ω·2ω²each mark is one step; a taller mark is a place with no step just before it4 order types, drawn by squeezing each run of steps into a finite width

show: "goodstein"

The Goodstein sequence from 3, with the ordinal beside each termA table of the Goodstein sequence with each term's hereditary representation and the ordinal obtained by replacing the base with omega.basevaluein hereditary baseordinal232 + 1ω + 1333ω4333522261117000G(3) written in hereditary base b, the base bumped to b+1, then one subtractedthe integers reach 0 after 5 steps, and the ordinals fall the whole way

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

The whole library · What the figures prove