Question

can you give an example of a linearly ordered set which has all suprema and infima but is not a well-order.

is the interval [-1,1] in real numbers a good example???

Answer 1

i think this is well ordered. maybe \((-1,1)\) is not

Answer 2

yes, the set must be closed and bounded for it to have all suprema and infima... so (-1, 1) won't work...

Answer 3

can you think of a better example or mine works??