If each A_i is a set containing infinite elements, and A_1 contains A_2 contains A_3 contains ... on and on, then is the intersection of all these sets infinite?
I think the intersection of all the sets is infinite cause cause no matter how far you go down the A_i's that particular A_i will contain infinite elements and the intersection of all the sets before it, and including it, will be equal to A_i. So is my reasoning correct? Because maybe maybe as i approaches infinity the sets somehow get smaller?
Sorry, what I meant to say was that after considering your example , I could not see how .
How I interpret your argument is that since if then .
I can't see how happens in your example.
You pointed out that the cardinality of the positive reals is greater than that of the natural numbers. Does this have to do with what I'm missing?
(I've had some exposure to countable/uncountable sets but not much.)