Set of Positive Rational Numbers

The mathematical set of positive rational numbers, defined as the set of numbers that can be written as a fraction of two integers and are non-negative. i.e. $$\\{\frac{p}{q} \ : \ p,q \ \in \ Z, \ p/q \ge 0, \ q \ne 0\\}$$ where \(Z\) is the set of integers.

Details

The $contains method does not work for the set of Rationals as it is notoriously difficult/impossible to find an algorithm for determining if any given number is rational or not. Furthermore, computers must truncate all irrational numbers to rational numbers.

See also

Other special sets: Complex, ExtendedReals, Integers, Logicals, Naturals, NegIntegers, NegRationals, NegReals, PosIntegers, PosNaturals, PosReals, Rationals, Reals, Universal

Super classes

set6::Set -> set6::Interval -> set6::SpecialSet -> set6::Rationals -> PosRationals

Methods

Public methods

• PosRationals$new()

• PosRationals$clone()

Inherited methods

• set6::Set$add()

• set6::Set$multiplicity()

• set6::Set$print()

• set6::Set$remove()

• set6::Set$summary()

• set6::Interval$isSubinterval()

• set6::SpecialSet$strprint()

• set6::Rationals$contains()

• set6::Rationals$equals()

• set6::Rationals$isSubset()

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Method new()

Create a new PosRationals object.

Usage

PosRationals$new(zero = FALSE)

Arguments

zero

logical. If TRUE, zero is included in the set.

Returns

A new PosRationals object.

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Method clone()

The objects of this class are cloneable with this method.

Usage

PosRationals$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.