what is the least upper bound and greatest lower bound of the set
?
I will start be admitting that I am new to this type of notation so if my answer sounds like nonsense then you are probably correct.
The intersection of those two intervals will be I guess this is a limit on the x values
now if in the domain then there are no real solutions.
I'm seeing 2 sets.
and
{x : x is Real, e^{x} <= 2}
OP doesn't specify any relation between these two sets so I think this is 2 problems.
= so
the LUB of the first set is clearly 3. The GLB is clearly
The LUB of the 2nd set = ln(2) as you noted. There is no lower bound on set 2 so there is no GLB.
Yes, I agree that this is two separate problems.
MelodyII is right that the first set is equivalent to the interval so its least upper bound is 3 and greatest lower bound is .
romset is, of course, using the fact that the logarithm is an increasing function: if b then
So if then . So there is no greatest upper bound on x and the least upper bound is ln(2).