represents the domain of strictly negative rational numbers, as in xNegativeRationals.


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


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Basic Examples  (3)

-2/3 is a negative rational number:

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

Find negative rational solutions of an equation:

Scope  (5)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which Reduce should work:

Test whether several numbers are negative rationals:

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

TraditionalForm formatting:

Properties & Relations  (4)

Membership in NegativeRationals is equivalent to membership in Rationals and negativity:

NegativeRationals contains NegativeIntegers:

NegativeRationals is contained in NegativeReals, Algebraics and Complexes:

NegativeRationals is disjoint from NonNegativeRationals and PositiveRationals:

Wolfram Research (2019), NegativeRationals, Wolfram Language function,


Wolfram Research (2019), NegativeRationals, Wolfram Language function,


Wolfram Language. 2019. "NegativeRationals." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2019). NegativeRationals. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_negativerationals, author="Wolfram Research", title="{NegativeRationals}", year="2019", howpublished="\url{}", note=[Accessed: 24-June-2024 ]}


@online{reference.wolfram_2024_negativerationals, organization={Wolfram Research}, title={NegativeRationals}, year={2019}, url={}, note=[Accessed: 24-June-2024 ]}