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ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Binary endorelation
Preordering relation
Partial ordering relation
Partially ordered set
Maximal element
Definition D668
Maximum element
Formulation 0
Let P=(X,) be a D1103: Partially ordered set such that
(i) X
A D2218: Set element mX is a maximum element in P if and only if xX:(x,m)
Formulation 1
Let P=(X,) be a D1103: Partially ordered set such that
(i) X
A D2218: Set element mX is a maximum element in P if and only if xX:xm
Formulation 2
Let P=(X,) be a D1103: Partially ordered set such that
(i) X
A D2218: Set element mX is a maximum element in P if and only if Xm
Children
D1822: Map maximum
D296: Set upper bound
Results
R1077: Maximum element is unique