In this house we believe:

Sets    exist

Sets with the same elements are equal

For any two sets, there’s a set containing both

Filtering a set makes a subset

A set of sets can be union’d into a set

The set of all subsets of a set, the powerset, exists

Sets can be infinite, like ℕ

Applying a function to the elements of a set makes a set

No set contains itself

A set’s elements can be put in order

There is no ∞ between the sizes of ℕ and the powerset of ℕ