represents the domain of non-positive rational numbers, as in x∈NonPositiveRationals.


NonPositiveRationals
represents the domain of non-positive rational numbers, as in x∈NonPositiveRationals.
Details

- x∈NonPositiveRationals evaluates immediately if x is a numeric quantity.
- Simplify[expr∈NonPositiveRationals,assum] can be used to try to determine whether an expression corresponds to a non-positive rational number under the given assumptions.
- (x1|x2|…)∈NonPositiveRationals and {x1,x2,…}∈NonPositiveRationals test whether all xi are non-positive rational numbers.
- The domain of non-positive integers is taken to be a subset of the domain of non-positive rationals.
- NonPositiveRationals is output in StandardForm or TraditionalForm as
. This typeset form can be input using
nprats
.
Examples
open all close allBasic Examples (3)
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 non-positive rationals:
If any number is explicitly not a non-positive rational, the result is False:
TraditionalForm formatting:
Properties & Relations (4)
Membership in NonPositiveRationals is equivalent to membership in Rationals and non-positivity:
NonPositiveRationals contains NonPositiveIntegers:
NonPositiveRationals is contained in NonPositiveReals, Algebraics and Complexes:
NonPositiveRationals is disjoint from PositiveRationals:
NonPositiveRationals intersects NonNegativeRationals:
Tech Notes
Related Guides
History
Text
Wolfram Research (2019), NonPositiveRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonPositiveRationals.html.
CMS
Wolfram Language. 2019. "NonPositiveRationals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonPositiveRationals.html.
APA
Wolfram Language. (2019). NonPositiveRationals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonPositiveRationals.html
BibTeX
@misc{reference.wolfram_2025_nonpositiverationals, author="Wolfram Research", title="{NonPositiveRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NonPositiveRationals.html}", note=[Accessed: 16-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_nonpositiverationals, organization={Wolfram Research}, title={NonPositiveRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NonPositiveRationals.html}, note=[Accessed: 16-August-2025]}