## Peano arithmetic

Giuseppe Peano's system for representing natural
numbers *inductively* using only two symbols, "0"
(zero) and "S" (successor).

This system could be expressed as a recursive data type with the following Haskell definition:

data Peano = Zero | Succ PeanoThe number three, usually written "SSS0", would be Succ (Succ (Succ Zero)). Addition of Peano numbers can be expressed as a simple syntactic transformation:

plus Zero n = n plus (Succ m) n = Succ (plus m n)

Last updated: 1995-03-28

### Nearby terms:

peak envelope power ♦ Peano ♦ **Peano arithmetic** ♦ PEARL ♦ Pebble ♦ Pebbleman

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