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What (who) is upper bound - definition
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 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)
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 .
least upper 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> (lub or "join", "supremum") The least upper bound of
two elements a and b is an upper bound c such that a <= c and
b <= c and if there is any other upper bound c' then c <= c'.
The least upper bound of a set S is the smallest b such that
for all s in S, s <= b. The lub of mutually comparable
elements is their maximum but in the presence of incomparable
elements, if the lub exists, it will be some other element
greater than all of them.
Lub is the dual to greatest lower bound.
(In LaTeX, "<=" is written as sqsubseteq, the lub of two
elements a and b is written a sqcup b, and the lub of set S
is written as igsqcup S).
(1995-02-03)
Wikipedia
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.
Examples of use of upper bound
1. "We have not seemed able to put an upper bound on that number." And there is another mostly unspoken fear.
2. Inflation, excluding food and energy prices, should rise by about 2 percent this year and wouldn’t exceed that upper bound next year.
3. That would be above even the upper bound of the central bank‘s uncertainty band, but still an encouraging turnaround after suffering simultaneous shocks.
4. As a result, annual inflation increased marginally from '.' percent in May to 10.1 percent, albeit remaining above the upper bound of the uncertainty band.
5. Prices have risen 2.8 percent since the start of 2007, and with previous forecasts for December inflation at around 0.2 percent, overall 2007 inflation would be 3 percent: exactly the upper bound of the government and the Bank of Israel‘s inflation target for the year.