represents the domain of non-positive real numbers.


  • xNonPositiveReals evaluates immediately if x is a numeric quantity.
  • Simplify[exprNonPositiveReals,assum] can be used to try to determine whether an expression corresponds to a non-positive real number under the given assumptions.
  • (x1|x2|)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.


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Basic Examples  (3)

is a non-positive real number:

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

Find non-positive real solutions of an equation:

Scope  (4)

Test if a numeric quantity is non-positive:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Test whether several numbers are non-positive reals:

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

Applications  (1)

Testing membership in the non-positive reals is a fast way to verify non-positivity of a large list:

Properties & Relations  (4)

Membership in NonPositiveReals is equivalent to membership in Reals along with non-positivity:

NonPositiveReals contains NonPositiveRationals and NonPositiveIntegers:

NonPositiveReals is contained in Complexes:

NonPositiveReals is disjoint from PositiveReals:

It intersects NonNegativeReals:

Wolfram Research (2019), NonPositiveReals, Wolfram Language function,


Wolfram Research (2019), NonPositiveReals, Wolfram Language function,


Wolfram Language. 2019. "NonPositiveReals." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2019). NonPositiveReals. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_nonpositivereals, author="Wolfram Research", title="{NonPositiveReals}", year="2019", howpublished="\url{}", note=[Accessed: 13-June-2024 ]}


@online{reference.wolfram_2024_nonpositivereals, organization={Wolfram Research}, title={NonPositiveReals}, year={2019}, url={}, note=[Accessed: 13-June-2024 ]}