Union Closed

Numerical endogamy—
Combine any pair and you get
A set already a member
Of the existing family.

Consider combinatorics,
Which is just counting elements.
A little surprise, a little
Information. Lots of surprise,

A lot. Now where are you going?
Search through elements one by one.
How much can you learn from each one?
Surprise, surprise. That’s quite a lot.

There’s a proof now. Works to a point.
No number’s ever a fair coin.