# NonNegativeIntegers

represents the domain of non-negative integers, as in xNonNegativeIntegers.

# Details

• xNonNegativeIntegers evaluates immediately if x is a numeric quantity.
• Simplify[exprNonNegativeIntegers,assum] can be used to try to determine whether an expression is a non-negative integer under the given assumptions.
• (x1|x2|)NonNegativeIntegers and {x1,x2,}NonNegativeIntegers test whether all xi are non-negative integers.
• NonNegativeIntegers is output in StandardForm or TraditionalForm as . This typeset form can be input using nnints.

# Examples

open allclose all

## Basic Examples(3)

Seven is a non-negative integer:

If is an integer, is a non-negative integer:

Find non-negative integer solutions of a Pell equation:

## Scope(6)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Solve an optimization problem over the non-negative integers:

Test whether several numbers are non-negative integers:

If any number is explicitly not a non-negative integer, the result is False:

## Applications(1)

Testing membership in the non-negative integers is a fast way to verify non-negativity of a large list:

## Properties & Relations(3)

Membership in NonNegativeIntegers is equivalent to membership in Integers and non-negativity:

NonNegativeIntegers is contained in NonNegativeReals and NonNegativeRationals:

NonNegativeIntegers is disjoint from NegativeIntegers:

It intersects NonPositiveIntegers:

Introduced in 2019
(12.0)