According to the Archimedean property, there exists one of these numbers larger than any given real number; and all inductive sets contain these numbers as a subset.
This set, a commutative monoid, is the domain of Landau's function as well as of the totient (TOH-shent) function, and numbers of this type can be written as the sum of other numbers of this type via a partition. According to the well-ordering principle, any subset of this set contains a least element. Multiplication and addition on this set are recursively defined along with a successor function by the Peano axioms. According to the Archimedean property, there exists one of these numbers larger than any given real number; and all inductive sets contain these numbers as a subset. Contained in both the rationals and the integers, name this set of the positive integers, denoted N.
This set, a commutative monoid, is the domain of Landau's function as well as of the totient (TOH-shent) function, and numbers of this type can be written as the sum of other numbers of this type via a partition.
{natural} numbers [or naturals; accept {N} before the end; prompt on {integers;} accept {positive integers}