Generator

chains

A generator in the logic library, called 7 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.

chains 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

A closed interval and an open one, matched point for pointTwo number lines, one closed and one open, with arrows showing the countable sequence of points that has to move.[0, 1](0, 1)01½0 goes to a half and 1/n goes to 1/(n+2); every other point of [0, 1] stays where it is8 moved points drawn, all distinct, all inside (0, 1) — and the two endpoints are gone

show: "sets"

Two injections shifted by 2 and 3, and the chains they cutTwo rows of dots with arrows for each injection, coloured by which chain each element belongs to.AB001122334455667788left to right adds 2, right to left adds 3; neither is onto and both are one-to-one5 chains in the window, and the assembled map is one-to-one on all of it

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