# PositiveRationals

represents the domain of strictly positive rational numbers, as in xPositiveRationals.

# Details

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

# Examples

open allclose all

## Basic Examples(3)

2/3 is a positive rational number:

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

Find positive 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 positive rationals:

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

## Properties & Relations(4)

Membership in PositiveRationals is equivalent to membership in Rationals along with positivity:

PositiveRationals contains PositiveIntegers:

PositiveRationals is contained in PositiveReals, Algebraics and Complexes:

PositiveRationals is disjoint from NonPositiveRationals and NegativeRationals:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_positiverationals, author="Wolfram Research", title="{PositiveRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PositiveRationals.html}", note=[Accessed: 27-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_positiverationals, organization={Wolfram Research}, title={PositiveRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/PositiveRationals.html}, note=[Accessed: 27-September-2023 ]}