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PositiveReals

PositiveReals

represents the domain of strictly positive real numbers.

Details

x∈PositiveReals evaluates immediately if x is a numeric quantity.
Simplify[expr∈PositiveReals,assum] can be used to try to determine whether an expression corresponds to a positive real number under the given assumptions.
(x₁|x₂|…)∈PositiveReals and {x₁,x₂,…}∈PositiveReals test whether all x_i are positive real numbers.
PositiveReals is output in StandardForm and TraditionalForm as . This typeset form can be input using preals.

Examples

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Basic Examples (3)

is a positive real number:

If is a real number, then is a positive real number:

Find positive real solutions of an equation:

Scope (4)

Test if a numeric quantity is positive:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Test whether several numbers are positive reals:

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

Applications (1)

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

Properties & Relations (4)

Membership in PositiveReals is equivalent to membership in Reals along with positivity:

PositiveReals contains PositiveRationals and PositiveIntegers:

PositiveReals is contained in Complexes:

PositiveReals is disjoint from NonPositiveReals and NegativeReals:

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