Prove that if X is a set of ordinals, then supX is an ordinal larger than all elements of X (and therefore not in X).
Any help would be much appreciated.
This is false and a good example of what's probably an ill-posed question: for example, the set $\displaystyle X=\{1,2\}$ of the first two ordinals has a maximum which is 2. The same with the set $\displaystyle X=\{1,2,7,\omega\}$, again we have a maximum which is $\displaystyle \omega$
Tonio