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NonPositiveReals

NonPositiveReals

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 x_i are non-positive real numbers.
NonPositiveReals is output in StandardForm and TraditionalForm as . This typeset form can be input using npreals.

Examples

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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:

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