Natural numbers are the counting numbers: 1, 2, 3, 4, ... (sometimes including 0).
Natural numbers (ℕ) are the most fundamental numbers, used for counting objects. There is some debate about whether 0 is included; in set theory and computer science it often is, while in number theory it often isn't. Natural numbers are closed under addition and multiplication but not under subtraction or division. They satisfy the Peano axioms, which provide a formal foundation for arithmetic.
Natural numbers were the first numbers used by humans, with evidence of tally marks on bones from 35,000 years ago. The Greek mathematician Pythagoras believed natural numbers had mystical properties. Giuseppe Peano axiomatized them in 1889 with five axioms.