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Let A be an ordered set and X a subset of A. An element b is called an upper bound for the set X if every element in X is less than or equal to b. If such an upper bound exists, the set X is called bounded above.

Let A be an ordered set, and X a subset of A. An element b in A is called a least upper bound (or supremum) for X if b is an upper bound for X and there is no other upper bound b' for X that is less than b. We write b = sup(X).

By its definition, if a least upper bound exists, it is unique.

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