On Mar 13, 1:56 pm, Snidely <snidely....@gmail.com> wrote: > DavidW scribbled something on Tuesday the 13th (redux): > > > No. You start giving me real numbers and for each one I'll give you an > > integer. We can keep doing that for as long as you like and I will never run > > out of integers. Now you'll probably say that you didn't really mean "larger" > > after all > > and want to bring up bijections and cardinality and such like. Save it. > > Or not. Part of the point is that for any two real real numbers you > give me an integer label for, I can find infinitely many real numbers > in between, innit? For any two integers, there are only finitely many > integers in between, no matter how large you make the integers.
That's not really the point, since the rational numbers are "dense" like the real numbers--you can find infinitely many of them between any pair--but there's a one-to-one correspondence between them and the integers.
Nevertheless, I will not be expelled from the paradise Cantor created for us. Not that I know it well at all.