The group of natural numbers is naturally even a rig – in fact the initial rig – and this multiplicative structure extends to to make it a ring – in fact the initial ring.
The underlying sets and are isomorphic. Some subcultures of mathematics (and not only set theorists) use the term ‘integer’ synonymously for a natural number. Computer scientists distinguish between ‘unsigned integers’ (natural numbers) and ‘signed integers’ (integers as described here). Translations can also cause confusion with the term ‘whole number’.
(A different common formalization of integers in type theory is in a binary notation, as in the Coq standard library. Binary notation is exponentially more efficient for performing computations, but the unary notation was convenient for calculating .)
Revised on July 23, 2014 04:19:45
by Urs Schreiber