# OrderedSetΒΆ

The class of totally ordered sets, that is, sets such that for each pair of elements `(a, b)`

exactly one of the following relations holds `a<b or a=b or b<a`

and the relation is transitive, i.e. `a<b and b<c => a<c`

. This order should be the natural order on given structure.

- <: (%, %) -> Boolean
- from PartialOrder
- <=: (%, %) -> Boolean
- from PartialOrder
- =: (%, %) -> Boolean
- from BasicType
- >: (%, %) -> Boolean
- from PartialOrder
- >=: (%, %) -> Boolean
- from PartialOrder
- ~=: (%, %) -> Boolean
- from BasicType
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory

- max: (%, %) -> %
`max(x,y)`

returns the maximum of`x`

and`y`

relative to`"<"`

.

- min: (%, %) -> %
`min(x,y)`

returns the minimum of`x`

and`y`

relative to`"<"`

.- smaller?: (%, %) -> Boolean
- from Comparable