DefinitionIn a together ordered, a maximum element is an element such as it does not exist any other element of this unit which is higher to him.
Dualement, one defines minimal element : element such as there does not exist any other element which is lower to him.
In mathematical language: either E an ordered unit, has is known as maximum element of E so for any X pertaining to E, has ≤ X → has = X
Caution: if the order is partial, a maximum element is not inevitably a Raising, nor the higher Borne of the unit.
- the real intervals of type '' have a single maximum element: B .
- the real intervals of type do not have a maximum element. ('' B '' is only one raising) * A tree provided with the relation “is an ancestor of” has as maximum elements all its sheets.
- upper Limit
- larger element
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