On Fri, May 27, 2011 at 3:14 PM, Levi Pearson <[email protected]> wrote: > Cardinal arithmetic can be used to show not only that the number of > points in a real number line is equal to the number of points in any > segment of that line, but that this is equal to the number of points > on a plane and, indeed, in any finite-dimensional space. These results > are highly counterintuitive, because they imply that there exist > proper subsets and proper supersets of an infinite set S that have the > same size as S, although S contains elements that do not belong to its > subsets, and the supersets of S contain elements that are not included > in it.
Is it possible to say what you just said in terms of injective, surjective, etc. functions? It sounds like this would only apply to countably infinite groups, but I may be mistaken about that as well. > The solution to the problem of how an infinite universe can expand > lies in first figuring out what you mean by 'infinite universe' and > what you mean by 'expand'. There is indeed a solution to this, given > appropriate definitions, which can be found on the 'Cosmology > Tutorial' page I linked in a different thread. I'm afraid I'll have to bookmark that, as I'm not able to devote more than a minute or two to my computer at any given time just now. It does look good though. /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
