NegRationals: Set of Negative Rational Numbers

In set6: R6 Mathematical Sets Interface

Description

The mathematical set of negative rational numbers, defined as the set of numbers that can be written as a fraction of two integers and are non-positive. 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 -> NegRationals

Methods

Public methods

• NegRationals$new()

• NegRationals$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 NegRationals object.

Usage

NegRationals$new(zero = FALSE)

Arguments

zero

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

Returns

A new NegRationals object.

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Method clone()

The objects of this class are cloneable with this method.

Usage

NegRationals$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

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

set6 documentation built on Oct. 18, 2021, 5:06 p.m.