represents the domain of strictly positive rational numbers, as in xPositiveRationals.


  • xPositiveRationals evaluates immediately if x is a numeric quantity.
  • Simplify[exprPositiveRationals,assum] can be used to try to determine whether an expression corresponds to a positive rational number under the given assumptions.
  • (x1|x2|)PositiveRationals and {x1,x2,}PositiveRationals test whether all xi are positive rational numbers.
  • The domain of positive integers is taken to be a subset of the domain of positive rationals.
  • PositiveRationals is output in StandardForm or TraditionalForm as TemplateBox[{}, PositiveRationals]. This typeset form can be input using prats.


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Basic Examples  (3)

2/3 is a positive rational number:

A sum of positive rational numbers is a positive rational number:

Find positive rational solutions of an equation:

Scope  (5)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which Reduce should work:

Test whether several numbers are positive rationals:

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

TraditionalForm formatting:

Properties & Relations  (4)

Membership in PositiveRationals is equivalent to membership in Rationals along with positivity:

PositiveRationals contains PositiveIntegers:

PositiveRationals is contained in PositiveReals, Algebraics and Complexes:

PositiveRationals is disjoint from NonPositiveRationals and NegativeRationals:

Introduced in 2019