I'd just like to take a 'debate' I was involved in on a previous forum regarding the nature of infinity.
People were debating (heatedly) whether there are more numbers between 0 and 1 than 1 and 2.
I invoked Cantor, and his concept of 'countability'. The set of all real numbers is uncountable, therefore it is a 'transfinity', which may or may not be smaller or larger than an infinity, but cannot be counted in such a way.
So, my position was that asking whether there's more numbers between 0 and 1 than 1 and 2 is meaningless since we cannot count them at all so no comparison can be made.
I just want a sanity check to make sure I'm not goofing up here - anybody got anything to add to that (or criticisms as to why I've completely got this wrong or something?!)
Whoops: Just read the infinities equations thread.. you guys are cool man, you've discussed things I find interesting even before I joined!
b.t.w. I think William is pretty much putting across the point I'm mentioned here, although in somewhat better detail. Three cheers for William!!