represents the domain of strictly positive real numbers.


  • xPositiveReals evaluates immediately if x is a numeric quantity.
  • Simplify[exprPositiveReals,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 xi are positive real numbers.
  • PositiveReals is output in StandardForm and TraditionalForm as . This typeset form can be input using preals.


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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:

Introduced in 2019