It's not true. If the field is and then the requirement is clearly satisfied by . However if we have .
Perhaps you need the extra condition that ?
Hey everyone, I've looked at this one for a while and just can't seem to get started. Anyone care to give me a hint / help out? Thanks!
Suppose that S is an ordered field. Define sqrt(a) to be the number such that (sqrt(a))^2 = a for a >= 0. Prove that if a,b are elements of S and 0 =< a =< b, then sqrt(a) =< sqrt(b)