NegativeRationals

NegativeRationals

represents the domain of strictly negative rational numbers, as in x∈NegativeRationals.

Details

  • x∈NegativeRationals evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈NegativeRationals,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.

Examples

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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, https://reference.wolfram.com/language/ref/NegativeRationals.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_negativerationals, author="Wolfram Research", title="{NegativeRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeRationals.html}", note=[Accessed: 09-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_negativerationals, organization={Wolfram Research}, title={NegativeRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeRationals.html}, note=[Accessed: 09-May-2025 ]}