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Lower and Upper bounds

LOWER AND UPPER BOUNDS

Upper Bound:  Let A  S, then an element s  S is called upper bound of A if and only if-
a ≤ s,  a  A.

Lower Bound: Let A  S, then an element s  S is called the lower bound of A is and only if-
 a,  a  A.

Least Upper Bound: If  S and g  S, then g is called the least upper bound of A if and only if the following two conditions hold-
a)     g is upper bound of the set A.
b)      s for every upper bound s of A.
The least upper bound of A is denoted by l.u.b.A or supA.

Greatest Lower Bound: If  S and l  S, then l is called the greatest lower bound of A if and only if the following two conditions hold-
a)     l is lower bound of the set A.
b)      l, for every lower bound s of A.


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