what is the least upper bound and greatest lower bound of the set

?

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- December 5th 2013, 01:01 AMTweetyGreatest lower and leat upper bound help
what is the least upper bound and greatest lower bound of the set

?

- December 5th 2013, 03:42 AMMelody2Re: Greatest lower and leat upper bound help
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. - December 5th 2013, 04:51 AMromsekRe: Greatest lower and leat upper bound help
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. - December 5th 2013, 07:28 AMHallsofIvyRe: Greatest lower and leat upper bound help
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). - December 8th 2013, 04:08 AMMelody2Re: Greatest lower and leat upper bound help
why is it called the least upper bound and not just the upper bound?

and

why is it called the greatest lower bound and not just the lower bound? - December 8th 2013, 05:29 AMPlatoRe: Greatest lower and leat upper bound help