SUPREMA AND INFIMA

We now introduce the notions of upper bound and lower bound for a set of real numbers. These ideas will be of utmost importance in later sections.

Definition 

Let S be a nonempty subset of R

(a) The set S is said to be bounded above if there exists a number u element R such that s last than or equal u for all s element S. Each such number u is called an upper bound of S; (b) The set S is said to be bounded below if there exists a number w element R such that w last than or equal s for all s elemen S. Each such number w is called a lower bound of S; (c) A set is said to be bounded if it is bounded above and bounded below. A set is said to be unbounded if it is not bounded

Read More