Set of Rational Numbers

The mathematical set of rational numbers, defined as the set of numbers that can be written as a fraction of two integers. i.e. $$\\{\frac{p}{q} \ : \ p,q \ \in \ Z, \ q \ne 0 \\}$$ 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, PosRationals, PosReals, Reals, Universal

Super classes

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

Methods

Public methods

• Rationals$new()

• Rationals$contains()

• Rationals$isSubset()

• Rationals$equals()

• Rationals$clone()

Inherited methods

• set6::Set$add()

• set6::Set$multiplicity()

• set6::Set$print()

• set6::Set$remove()

• set6::Set$summary()

• set6::Interval$isSubinterval()

• set6::SpecialSet$strprint()

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Method new()

Create a new Rationals object.

Usage

Rationals$new(lower = -Inf, upper = Inf, type = "()")

Arguments

lower

numeric. Where to start the set. Advised to ignore, used by child-classes.

upper

numeric. Where to end the set. Advised to ignore, used by child-classes.

type

character Set closure type. Advised to ignore, used by child-classes.

Returns

A new Rationals object.

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Method contains()

Method not possible for Rationals.

Usage

Rationals$contains(...)

Arguments

...

Ignored

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Method isSubset()

Method not possible for Rationals.

Usage

Rationals$isSubset(...)

Arguments

...

Ignored

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Method equals()

Method not possible for Rationals.

Usage

Rationals$equals(...)

Arguments

...

Ignored

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Method clone()

The objects of this class are cloneable with this method.

Usage

Rationals$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.