I am aware a set is Bounded if it has both upper and Lower bound and i know what a Limit point of a set is but how can i show that If S ⊂ R be a "bounded infinite set", then S' ≠∅

 

A "bounded infinite set" is a discrete (finite) subset of an infinite set as opposed to a discrete subset of a discrete set.

 

 

Eg

finite set {alphabet} discrete subset {letters a - g}

infinite set {integers} discrete subset {0 - 20}

A "bounded infinite set" is a discrete (finite) subset of an infinite set as opposed to a discrete subset of a discrete set.

 

 

Eg

finite set {alphabet} discrete subset {letters a - g}

infinite set {integers} discrete subset {0 - 20}

 

Careful here.

 

Both the sets [0,1] and (0,1) are infinite bounded subsets of R.

 

The question is surely fairly trivial since R is unbounded (1)

 

So partitioning R into subsets S and S' where S' is the null set and S is R is contradicts (1)

 

Sheff, Is this homework???

 

I will leave you to finish off formally, moderators may move this to the homework section.

Yea this is a homework bro which i must turn in on Monday. Thanks for the Insights.