This question has been bothering me for some while now and I still can't figure it out:
Prove that: (1) without the choice-axiom.
The way is defined in my courses is the following:
Let (where R is a wellorder on A).
Then ( is a ordinal and the ordertype of x)
I define: to be the set of all initial segments of A with respect to the wellorder R, wich is well-ordered by
Now is defined by not an injection?
In this case the (1) would become trivial, so I expect it's not. But Why?
It seems evidently true that and