Question

give an example of a well-ordered set which does not have all infima and suprema.
HELP!!

Answer 1

How about (0,1)? Any sequence in the set that converges to zero will have that as an inf, but it is not in the set. Similarly for sups at one. It's been a few years since I studied this, but I think you might at least get a start by thinking about an open interval as a possible solution.

Answer 2

so (0,1) in natural numbers?

Answer 3

I was thinking in the reals. The real numbers are well-ordered, aren't they?

Answer 4

the open interval (0, 1) does not contain a least element in the reals, so it is not well ordered...

Answer 5

Sorry, I told you it has been a while....

Answer 6

no prob... thx for trying to help anyway!