Re: surjective maps in general

Is it true that, for any *surjective* map of sets A
-> B,
that |A| >= |B| ?


Yes, more or less by definition; See

http://en.wikipedia.org/wiki/Cardinality

Given a surjective map f: A --> B, you can easily construct an injective map g: B --> A by choosing element h_b in f^{-1}(b) for all b in B and setting g(b) = h_b. (Unless I'm mistaken, this requires the axiom of choice)

-- Martin Wanvik
.