Hi can I get some help with the following theorem I need to prove:
Let A be a subset of the ordered set X. If A has an upper bound then A has a least upper bound..
Thanks!
I think it can be done this way:If A has an upper bound then A has a least upper bound.
From the question we know that A has an upper bound. Let's suppose A has two upper bounds and with .
( is also valid but i've decided to choose ).
Hence A has a least upper bound which is .