I think my question is generalized version of Uncountable minus countable set is uncountable
I have to show: if $A$ is an infinite set, and $B$ is a subset of $A$, which satisfies $|B|<|A|$, then $|A-B|=|A|$.
I understood the answer to the link above. My textbook advised me to use Axiom of Choice, but I don't know how to apply it into this theorem.
Recall the axiom of choice implies that summing two cardinals, for infinite cardinals, is the same as taking the $\max$.
Now recall that $|A|=|A-B|+|B|$.