1

1 is the next natural number after 0. In the system of Von Neumann ordinals and Zermelo's formalization of the natural numbers, it is represented by the set \(0+1 = \{\{\}\}\), while in the logical formalization of natural numbers it is identified with the proper class of singletons. Also, as a Church numeral, it is identified with the lambda calculus expression \(\lambda f. \lambda x. f(x)\).

1 is the least additive principal ordinal, being equal to \(\omega^0\), and as such is the least ordinal with a nonempty CNF representation.

It is equal to the identity in the monoid of natural numbers under multiplication.