2 · Compare three kinds of probes

These diagrams show finite stages of a halving probe, an approaching sequence, and a base-p probe. Every box has a precise parent in the stage above it.

Try this. Choose a probe and add stages. Select a box to highlight all the smaller boxes inside it. Compare how the number of boxes changes from one stage to the next.

Definition 1.2 describes these probes as inverse systems of finite sets. The activity calculates their stage sizes and fibres, and the tests compare those calculations with the Python implementation.