The intersection of the rationals in (0,1) and (0.5,7.5) is just the set of rationals in (0.5,7.5), unless I have misunderstood the question.
There are aleph-naught rationals in any interval which contains 2 rationals (e.g. is not (1,1) or [2,2] ). The rationals in the finite interval (a,b) can be placed into a bijection with the natural numbers by counting the integers by listing all multiples of 1 in (a,b) in increasing order, then all the multiples of 1/2 that are not already in the list, then multiples of 1/3 etc.
________________________________ From: mathCurious <firstname.lastname@example.org> To: email@example.com Sent: Wednesday, May 1, 2013 9:09 AM Subject: Re: RE: How does infinitesimal exist?
Specifically what is right? I am saying that if I am interpreting all this correctly (I am not positive on this point, hence I am posting here to ask) you end up finding an infinity that is less than aleph-naught, which contradicts what I interpret this article (http://en.wikipedia.org/wiki/Aleph_number) to be saying when it says that aleph-naught is the smallest infinite cardinal. Hence I am confused. Am I making some error here? BTW, I know who Cantor is. Thanks again for answering.