# FiniteΒΆ

The category of domains composed of a finite set of elements. We include the functions lookup and index to give a bijection between the finite set and an initial segment of positive integers.

- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- convert: % -> InputForm
- from ConvertibleTo InputForm

- enumerate: () -> List %
`enumerate()`

returns list of elements of the set.- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory

- index: PositiveInteger -> %
`index(i)`

takes a positive integer`i`

less than or equal to`size()`

and returns the`i`

`-`

th element of the set. This operation establishes a bijection between the elements of the finite set and`1..size()`

.- latex: % -> String
- from SetCategory

- lookup: % -> PositiveInteger
`lookup(x)`

returns a positive integer such that`x = index lookup x`

.

- random: () -> %
`random()`

returns a random element from the set.

- size: () -> NonNegativeInteger
`size()`

returns the number of elements in the set.- smaller?: (%, %) -> Boolean
- from Comparable