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

• Oct 3rd 2012, 07:34 PM
funnybabe
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
• Oct 3rd 2012, 09:27 PM
chiro
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?
• Oct 4th 2012, 06:20 AM
funnybabe
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?
• Oct 4th 2012, 04:30 PM
chiro
Re: glb and lub (greatest lower bound and least upper bound)
Sounds good!