A "least upper bound" for a set is then an upper bound that is as small as possible. That is, it is an upper bound that is smaller than every other upper bound. Greatest lower bounds are defined similarly. Definition: Let be a subset of that is bounded above.

What is a least upper bound example?

Any number that is greater than or equal to all of the elements of the set. The smallest of all upper bounds of a set of numbers. For example, the least upper bound of the interval (5,7) is 7 .

How do you find the least upper bound?

Definition 6 A least upper bound or supremum for A is a number u ∈ Q in R such that (i) u is an upper bound for A; and (ii) if U is another upper bound for A then U ≥ u. If a supremum exists, it is denoted by supA. Example 7 If A = [0,1] then 1 is a least upper bound for A.