0 a whole number (= a number such as 1, 3, or 17, that has no fractions and no digits after the decimal point) that is greater than zero, or sometimes that includes zero itself --
As an added benefit, proofs - naturally tree-structured - need not be arbitrarily linearized just so that natural number recursion and induction can be performed on them.
Similarly, rational numbers are traditionally formalised as pairs consisting of an integer, and a positive natural number.
The predicate that decides whether a natural number is even or not may be defined as follows.
If such a natural number does not exist, we say that the degree of is infinite.
Each of these events also carries a natural number as a parameter.
The functor preserves finite products and the natural number object (up to isomorphism).
The function at denotes list indexing and rev k computes the bit-reversal of a natural number.
The ' natural number ' approach is only one way to allow multivalued features.
