For any pair of sets A and B, we can define A≤B iff there exists injection f:A→B. I am trying prove that (A≤B)∨(B≤A).
I have tried assuming ¬(A≤B), then proving B≤A by constructing the required injection, but I haven't been able to make any progress. Any hints, etc. would be appreciated.
EDIT
Assuming ¬(A≤B), can you prove there exists a surjection f:A→B? Then it would be easy, by applying AC, to construct an injection g:B→A
No comments:
Post a Comment