glb and lub (greatest lower bound and least upper bound)

Greetings all,

I have a question that says S is a bounded set of real numbers and that lub S and glb S are equal. The question wants to know what you can conclude about S (the set).

my understanding is that glb and lub are both unique numbers and therefore do not equal. The only thing I could think of is that S only contains one number like (0,0) or (5,5) but then I thought maybe in that case there is no glb lub

thanks

Paula

Re: glb and lub (greatest lower bound and least upper bound)

Hey funnybabe.

The only other thing that builds on top of what you have said is that a set can only contain unique elements (no duplicates). So based on this, what can you say at least about the cardinality of the set?

Re: glb and lub (greatest lower bound and least upper bound)

the cardinality is 1 so there should only be 1 number in the set?

Re: glb and lub (greatest lower bound and least upper bound)