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They call the piece a Set, the basic boundary between an Inside and an Outside.

I like to tell the creation story of numbers, something like this:

Let a Set which bounds nothing and excludes everything be named Zero.

Let every Set after it bind together the preceding Set, and a Set of the preceding Set.

From this simple duet, a floodgate to the Naturals opens. One is the Set which bounds the Zero; Two is the set which bounds Zero, One, and Two. So on and so forth. A countable infinity of numerals, each unique and orderable, born from drawing boundaries between Insides and Outs.

To make the Negatives, first examine their true nature: the difference between two naturals. To make Negative One, bind together One and Two, or Two and Three, or Three and Four… The floodgates now point in two directions, and the Integers were born. . Rationals are pairs of Integers, bound in fractions. Half is One and Two, or Two and Four, or Three and Six… The steppes of numbers become smooth slopes.

Reals are harder to define: A pair of two infinite sets of Rationals, one binding all that’s less than the Real, the other binding all that’s more. They race like Zeno towards each other, converging from opposite ends, Negative and Positive Infinities, after an eternity, onto their final destination.

Pair the two Reals, and out come the Complexes. Pair four, Quaternions. Pair every number in an infinity of them to another to get maps and functions. Flip the definitions on their heads to get p-adic numbers, a separate breed of beasts who behave like nothing else. From a set, a universe.