NonPositiveReals
✖
NonPositiveReals
Details

- x∈NonPositiveReals evaluates immediately if x is a numeric quantity.
- Simplify[expr∈NonPositiveReals,assum] can be used to try to determine whether an expression corresponds to a non-positive real number under the given assumptions.
- (x1x2…)∈NonPositiveReals and {x1,x2,…}∈NonPositiveReals test whether all xi are non-positive real numbers.
- NonPositiveReals is output in StandardForm and TraditionalForm as
. This typeset form can be input using
npreals
.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
is a non-positive real number:

https://wolfram.com/xid/0bniuqomv1mm5-bur9kd

If is a real number,
is a non-positive real number:

https://wolfram.com/xid/0bniuqomv1mm5-d83wh7

Find non-positive real solutions of an equation:

https://wolfram.com/xid/0bniuqomv1mm5-hr5ijl

Scope (4)Survey of the scope of standard use cases
Test if a numeric quantity is non-positive:

https://wolfram.com/xid/0bniuqomv1mm5-yalfdo

Make domain membership assumptions:

https://wolfram.com/xid/0bniuqomv1mm5-ngh5dk


https://wolfram.com/xid/0bniuqomv1mm5-oaezsv

Specify the default domain over which a function should work:

https://wolfram.com/xid/0bniuqomv1mm5-g9ic3l


https://wolfram.com/xid/0bniuqomv1mm5-muk485

Test whether several numbers are non-positive reals:

https://wolfram.com/xid/0bniuqomv1mm5-3pjyzh

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

https://wolfram.com/xid/0bniuqomv1mm5-m7ag79

Applications (1)Sample problems that can be solved with this function
Properties & Relations (4)Properties of the function, and connections to other functions
Membership in NonPositiveReals is equivalent to membership in Reals along with non-positivity:

https://wolfram.com/xid/0bniuqomv1mm5-bus6sg

NonPositiveReals contains NonPositiveRationals and NonPositiveIntegers:

https://wolfram.com/xid/0bniuqomv1mm5-culh0e


https://wolfram.com/xid/0bniuqomv1mm5-v8w60t

NonPositiveReals is contained in Complexes:

https://wolfram.com/xid/0bniuqomv1mm5-ciam4c

NonPositiveReals is disjoint from PositiveReals:

https://wolfram.com/xid/0bniuqomv1mm5-pe30t4

It intersects NonNegativeReals:

https://wolfram.com/xid/0bniuqomv1mm5-ynhnih

Wolfram Research (2019), NonPositiveReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonPositiveReals.html.
Text
Wolfram Research (2019), NonPositiveReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonPositiveReals.html.
Wolfram Research (2019), NonPositiveReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonPositiveReals.html.
CMS
Wolfram Language. 2019. "NonPositiveReals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonPositiveReals.html.
Wolfram Language. 2019. "NonPositiveReals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonPositiveReals.html.
APA
Wolfram Language. (2019). NonPositiveReals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonPositiveReals.html
Wolfram Language. (2019). NonPositiveReals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonPositiveReals.html
BibTeX
@misc{reference.wolfram_2025_nonpositivereals, author="Wolfram Research", title="{NonPositiveReals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NonPositiveReals.html}", note=[Accessed: 06-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_nonpositivereals, organization={Wolfram Research}, title={NonPositiveReals}, year={2019}, url={https://reference.wolfram.com/language/ref/NonPositiveReals.html}, note=[Accessed: 06-June-2025
]}