Set of Positive Rational Numbers

Description

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.

p/q : p,q ε Z, p/q ≥ 0, q != 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.

Super classes

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

Methods

Public methods

• PosRationals$new()

• PosRationals$clone()

Method new()

Create a new PosRationals object.

Usage

PosRationals$new(zero = FALSE)

Arguments

Returns

A new PosRationals object.

Method clone()

The objects of this class are cloneable with this method.

Usage

PosRationals$clone(deep = FALSE)

Arguments

See Also

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