For example, the mathematical type "integer" contains the set of integers {..., -1, -2, -1, 0, 1, 2, 3, ...} together with operations +, -, *, /, <, <=, etc.

{..., -1, -2, -1, 0, 1, 2, 3, ...}

and the "natural numbers", or "nat", consists of the nonnegative integer {0, 1, 2, 3, ...} together with operations +, -, *, /, <, <=, etc.

{0, 1, 2, 3, ...}