> Though its binary representation may be more familiar, the formal mathematical construction of the integers consists of an equivalence class of pairs of natural numbers.

That's an elegant construction. It's interesting how different number sets can derived from pairs of a "smaller" set, equivalence classes, or both.

    integers: equivalence classes of pairs of naturals
    rationals: equivalence classes of pairs of integers
    reals: equivalence classes of Cauchy series on rationals
    complex numbers: pairs of reals

It's quite thought provoking to arrive at the construction of complex numbers just by counting apples.