What numbers are made of

According to how numbers (and more generally, ordinals) are defined by Zermelo and von Neumann, they are literally made of nothing.

In developing axioms for set theory, Zermelo used the sets 0, {0}, {{0}}, {{{0}}, {{{{0}}}} and so on as natural numbers. Here, 0 is the empty set, while S is an operator that defines the number following the input as the set that contains all the sets represented by the input.