Question

Math Analysis Problem.

Note: Inf S is a lower bound of a set.

Sup S is a upper bound and any smaller is not.

rone

Here is the key

Please help.

Answer 1

Let S subsetequalto R be a non- empty set sub if s a elementof R is said to be sub of s if s lessthanorequalto a for all s elementof S (ii). For each elementof greaterthan 0 theref exist at least one s elementof S suchthat a - elementof greaterthan 0 there exist at least one s elementof S such that a - elementof < S Inf of S: b elementof R is said to be inf of S if (i). b lessthanorequalto s for all s elementof S (ii). For each elementof greaterthan 0 there exist s elementof S such that B s < b + elementof Here, S = { 1/n}^infinity_n = 1 clearly 1/n lessthanorequalto 1 for all n greaterthanorequalto 1 Let elementof greaterthan 0, then 1 elementof S such that 1 - elementof < 1 Hence, sup S = 1 Clearly 0 < 1/n for all n greaterthanorequalto 1 let E > 0 be given.