Yes, I see this now.
I guess I was trying to find the distinction in meaning between the symbols \infty and \aleph_0. Would I be right in thinking that while \aleph_0 is the cardinality of the set of integers (amongst others), \infty is (potentially at least) an arbitrarily large member of that...
Well yes that is what I meant by size.
Should that be the first infinite cardinal? Surely finite sets also have cardinality, so the first cardinal would be 0, being the cardinality of the empty set.
Yes it all helps, and I appreciate all of the responses.
I have to do some work now :grumpy...
Are you sure about that? The entry in Wikipedia (!) on p-adics (http://en.wikipedia.org/wiki/P-adic_number) indicates otherwise (see I've been doing my homework :wink:). It seems to me you are referring to 10-adic integers.
What about in the context of set theory. Could \infty mean the size of the set of integers (= aleph-0)? I can see from previous discussion that it could not be an element of that set.
I don't quite follow this. By -1/9 I take it you are denoting the number that could also be represented as the recurring decimal -0.1111 ... But how can that be if the latter denotes a real number while ...111 doesn't denote anything at all in our usual number systems. (I'm being careful not to...
Hoping I may be permitted to make a belated contribution here.
Summarising the key points from some of the other posts:
The key to the problem is that the new 'number' generated by the diagonal argument will have an infinite number of non-zero digits resulting from the infinite number of...