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NonPositiveReals
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NonPositiveReals

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represents the domain of non-positive real numbers.

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.
  • (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.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

is a non-positive real number:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-bur9kd
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-d83wh7
Out[1]=1

Find non-positive real solutions of an equation:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-hr5ijl
Out[1]=1

Scope  (4)Survey of the scope of standard use cases

Test if a numeric quantity is non-positive:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-yalfdo
Out[1]=1

Make domain membership assumptions:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-ngh5dk
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-oaezsv
Out[2]=2

Specify the default domain over which a function should work:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-g9ic3l
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-muk485
Out[2]=2

Test whether several numbers are non-positive reals:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-3pjyzh
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-m7ag79
Out[2]=2

Applications  (1)Sample problems that can be solved with this function

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

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-ba3dco
In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-jx06
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bniuqomv1mm5-fodr0m
Out[3]=3

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:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-bus6sg
Out[1]=1

NonPositiveReals contains NonPositiveRationals and NonPositiveIntegers:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-culh0e
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-v8w60t
Out[2]=2

NonPositiveReals is contained in Complexes:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-ciam4c
Out[1]=1

NonPositiveReals is disjoint from PositiveReals:

In[1]:=1
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https://wolfram.com/xid/0bniuqomv1mm5-pe30t4
Out[1]=1

It intersects NonNegativeReals:

In[2]:=2
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https://wolfram.com/xid/0bniuqomv1mm5-ynhnih
Out[2]=2
Wolfram Research (2019), NonPositiveReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonPositiveReals.html.
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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.

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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.

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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

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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: 20-June-2025 ]}

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@misc{reference.wolfram_2025_nonpositivereals, author="Wolfram Research", title="{NonPositiveReals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NonPositiveReals.html}", note=[Accessed: 20-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: 20-June-2025 ]}

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@online{reference.wolfram_2025_nonpositivereals, organization={Wolfram Research}, title={NonPositiveReals}, year={2019}, url={https://reference.wolfram.com/language/ref/NonPositiveReals.html}, note=[Accessed: 20-June-2025 ]}