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NonNegativeIntegers

represents the domain of non-negative integers, as in x∈NonNegativeIntegers.

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Scope  
Applications  
Properties & Relations  
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NonNegativeIntegers

NonNegativeIntegers

represents the domain of non-negative integers, as in x∈NonNegativeIntegers.

Details

  • x∈NonNegativeIntegers evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈NonNegativeIntegers,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 TemplateBox[{}, NonNegativeIntegers]. This typeset form can be input using nnints.

Examples

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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:

TraditionalForm formatting:

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:

Wolfram Research (2019), NonNegativeIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/NonNegativeIntegers.html.

Text

Wolfram Research (2019), NonNegativeIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/NonNegativeIntegers.html.

CMS

Wolfram Language. 2019. "NonNegativeIntegers." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonNegativeIntegers.html.

APA

Wolfram Language. (2019). NonNegativeIntegers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonNegativeIntegers.html

BibTeX

@misc{reference.wolfram_2025_nonnegativeintegers, author="Wolfram Research", title="{NonNegativeIntegers}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NonNegativeIntegers.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_nonnegativeintegers, organization={Wolfram Research}, title={NonNegativeIntegers}, year={2019}, url={https://reference.wolfram.com/language/ref/NonNegativeIntegers.html}, note=[Accessed: 08-August-2025]}