MATH.16:2 - Problem

A familiar notation can suggest an object without explaining why it has the right structure. A pair of entries, a sequence, an equivalence class and a tagged alternative may all hold related information, yet the operations available on them differ.

Even an apparently adequate requirement can leave the object underdetermined. An object from which two entries can be recovered might also contain an extra entry. To say that the first two entries determine the whole, we need a further condition. Without it, a later map may require information that the proposed construction never supplied.

The problem is to turn the intended use into a mathematical specification, construct an object that satisfies it, and derive the maps and comparisons needed next.