PositiveRationals
✖
PositiveRationals
represents the domain of strictly positive rational numbers, as in x∈PositiveRationals.
Details
- x∈PositiveRationals evaluates immediately if x is a numeric quantity.
- Simplify[expr∈PositiveRationals,assum] can be used to try to determine whether an expression corresponds to a positive rational number under the given assumptions.
- (x1x2…)∈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 allBasic Examples (3)Summary of the most common use cases
Scope (5)Survey of the scope of standard use cases
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:
TraditionalForm formatting:
Properties & Relations (4)Properties of the function, and connections to other functions
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.
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.
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
Wolfram Language. (2019). PositiveRationals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PositiveRationals.html
BibTeX
@misc{reference.wolfram_2024_positiverationals, author="Wolfram Research", title="{PositiveRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PositiveRationals.html}", note=[Accessed: 10-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_positiverationals, organization={Wolfram Research}, title={PositiveRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/PositiveRationals.html}, note=[Accessed: 10-January-2025
]}