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.

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- Oct 25th 2009, 07:59 PMqwe123Help with ordinals
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. - Oct 25th 2009, 08:29 PMtonio

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