Thanks for the really fast reply. I've got another related question.
1. If A is a subset of B and B is countable, then A is at most countable?
If 1 is correct, then A is either finite or countable by definition.
2. What if A is known to be infinite,then is it safe to say A is countable...
Question is the same as the title.
What I think is that since every countable set C ~ Z+( all positive integers) and Z+ is infinite, then C is also infinite. Sounds straightfoward but I need to check it.
Thanks,
Ronn
Hello.
I have a question about Dedekind' cut.
Problem #20 of Baby rudin's p23 asks: prove why axiom (A5) on page 5 fails if cuts had maximum elements.
(A5): To every x in F( a field) corresponds an element -x in F such that x + (-x) = 0.
I guess Archimedean property is a starting...