# NegativeRationals

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

# Details

• 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 . 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:

## 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_2024_negativerationals, author="Wolfram Research", title="{NegativeRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeRationals.html}", note=[Accessed: 24-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_negativerationals, organization={Wolfram Research}, title={NegativeRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeRationals.html}, note=[Accessed: 24-June-2024 ]}