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NonNegativeRationals

represents the domain of non-negative rational numbers, as in x∈NonNegativeRationals.

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NonNegativeRationals

NonNegativeRationals

represents the domain of non-negative rational numbers, as in x∈NonNegativeRationals.

Details

  • x∈NonNegativeRationals evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈NonNegativeRationals,assum] can be used to try to determine whether an expression corresponds to a non-negative rational number under the given assumptions.
  • (x1|x2|…)∈NonNegativeRationals and {x1,x2,…}∈NonNegativeRationals test whether all xi are non-negative rational numbers.
  • The domain of non-negative integers is taken to be a subset of the domain of non-negative rationals.
  • NonNegativeRationals is output in StandardForm or TraditionalForm as TemplateBox[{}, NonNegativeRationals]. This typeset form can be input using nnrats.

Examples

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Basic Examples  (3)

2/3 is a non-negative rational number:

Wolfram Language code: Element[2 / 3, NonNegativeRationals]

A sum of non-negative rational numbers is a non-negative rational number:

Wolfram Language code: Simplify[x + y∈NonNegativeRationals, (x | y)∈NonNegativeRationals]

Find non-negative rational solutions of an equation:

Wolfram Language code: Reduce[(2x ^ 2 - 1)(4x ^ 2 - 1) == 0, x, NonNegativeRationals]

Scope  (5)

Test domain membership of a numeric expression:

Wolfram Language code: Element[21 / 32, NonNegativeRationals]
Wolfram Language code: Element[0, NonNegativeRationals]
Wolfram Language code: Element[Pi, NonNegativeRationals]

Make domain membership assumptions:

Wolfram Language code: Refine[x^2 + 2 x y + (y^3/3)∈NonNegativeRationals, (x | y)∈NonNegativeRationals]

Specify the default domain over which Reduce should work:

Wolfram Language code: Reduce[(x ^ 2 - 4 / 9)(x ^ 3 - 2) == 0, x, NonNegativeRationals]

Test whether several numbers are non-negative rationals:

Wolfram Language code: (x | y | 1 / 2)∈NonNegativeRationals

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

Wolfram Language code: {x, y, -1 / 2}∈NonNegativeRationals

TraditionalForm formatting:

Wolfram Language code: NonNegativeRationals//TraditionalForm

Properties & Relations  (4)

Membership in NonNegativeRationals is equivalent to membership in Rationals and non-negativity:

Wolfram Language code: x∈NonNegativeRationals

NonNegativeRationals contains NonNegativeIntegers:

Wolfram Language code: Refine[x∈NonNegativeRationals, x∈NonNegativeIntegers]

NonNegativeRationals is contained in NonNegativeReals, Algebraics and Complexes:

Wolfram Language code: Refine[x∈NonNegativeReals, x∈NonNegativeRationals]
Wolfram Language code: Refine[x∈Algebraics, x∈NonNegativeRationals]
Wolfram Language code: Refine[x∈ℂ, x∈NonNegativeRationals]

NonNegativeRationals is disjoint from NegativeRationals:

Wolfram Language code: Reduce[x∈NegativeRationals, x, NonNegativeRationals]

NonNegativeRationals intersects NonPositiveRationals:

Wolfram Language code: Reduce[x∈NonPositiveRationals, x, NonNegativeRationals]
Wolfram Research (2019), NonNegativeRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonNegativeRationals.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_nonnegativerationals, author="Wolfram Research", title="{NonNegativeRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NonNegativeRationals.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_nonnegativerationals, organization={Wolfram Research}, title={NonNegativeRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NonNegativeRationals.html}, note=[Accessed: 13-June-2026]}