R: Set of Negative Rational Numbers

NegRationals {set6} | R Documentation

## Set of Negative Rational Numbers

### 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()`

#### 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.

#### 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`

[Package set6 version 0.2.0 Index]