I would appreciate help with two questions:
i) a,b,c ordinals. Derive the following cancellation law: a+b=a+c implies b=c.
I can show this by induction, but I don't think that comes under the heading of "derive". How can this be derived from axioms/ definitions etc?
ii) I have to find which possibility holds out of a<b, a=b, b<a when a=(w+1).w and b=w.(w+1) (w=omega).
Now, by distributive laws of ordinals, b=w^2+w. I can show that a>w^2 (since w+1>w implies (w+1).w>w^2. However, all this shows is that both a and b are greater than w^2, which doesn't really help. Any ideas?