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Τι (ποιος) είναι greatest lower bounds - ορισμός

EVERY ELEMENT OF A PARTIALLY ORDERED SET A WHICH IS GREATER (RESP. LOWER) THAN EVERY ELEMENT OF A SUBSET B INCLUDED IN A

Lower bound; Upper bounds; Upper Bound; Upper bound; Upper Bound and Lower Bound; Upper and lower bound; Upper & lower bounds; Tight upper bound; Tight lower bound; Lower and upper bounds; Majorant; Majorized set; Minorant; Minorized; Minorized set; Sharp bound

Upper and lower bounds

In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of .

https://en.wikipedia.org/wiki/Upper_and_lower_bounds

upper bound

An upper bound of two elements x and y under some relation <= is an element z such that x <= z and y <= z. ("<=" is written in LaTeX as sqsubseteq). See also least upper bound. (1995-02-15)

greatest lower bound

LEAST (RESP. GREATEST) OF MAJORING (RESP. MINORING) ELEMENTS OF A PARTIALLY ORDERED SET (NOT NECESSARILY EXISTING IN ALL SETS)

Supremum; Least upper bound; Greatest lower bound; Suprema; Infima; LUB; Lowest upper bound axiom; Smallest upper bound; Infimum; Infima and suprema; Supremum and infimum

<theory> (glb, meet, infimum) The greatest lower bound of two elements, a and b is an element c such that c <= a and c <= b and if there is any other lower bound c' then c' <= c. The greatest lower bound of a set S is the greatest element b such that for all s in S, b <= s. The glb of mutually comparable elements is their minimum but in the presence of incomparable elements, if the glb exists, it will be some other element less than all of them. glb is the dual to least upper bound. (In LaTeX "<=" is written as sqsubseteq, the glb of two elements a and b is written as a sqcap b and the glb of set S as igsqcap S). (1995-02-03)

Βικιπαίδεια

Upper and lower bounds

In mathematics, particularly in order theory, an upper bound or majorant of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S.Dually, a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S. A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.

https://en.wikipedia.org/wiki/Upper and lower bounds