# OrderedSetΒΆ

catdef.spad line 1120 [edit on github]

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 PartialOrder

- >: (%, %) -> Boolean
from PartialOrder

- 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