# solvelib::BasicSet

Basic infinite sets

## Syntax

### Domain Creation

`solvelib::BasicSet(`Dom::Integer`)`
`solvelib::BasicSet(`Dom::Rational`)`
`solvelib::BasicSet(`Dom::Real`)`
`solvelib::BasicSet(`Dom::Complex`)`

## Description

The domain `solvelib::BasicSet` comprises the four sets of integers, reals, rationals, and complex numbers, respectively.

The four basic sets are assigned to the identifiers `Z_`, `Q_`, `R_`, and `C_` during system initialization.

The set of positive integers, too, is assigned to the identifier `N_` during system initialization. It is not represented by a basic set but by the intersection of `Z_` and the interval ```Dom::Interval([1], infinity)```.

## Superdomain

`Dom::BaseDomain`

## Axioms

`Ax::canonicalRep`

## Categories

`Cat::Set`

## Examples

### Example 1

The domain of basic sets know about the basic arithmetical and set-theoretic functions:

```J:=Dom::Interval(3/2, 21/4): Z_ intersect J```

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## Mathematical Methods

### `contains` — Test whether some object is a member

`contains(a, S)`

Equivalently, `is(a in S)` may be used.

## Conversion Methods

### `convert` — Convert a domain into a basic set

`convert(d)`

### `set2prop` — Convert a set to a property

`set2prop(S)`