```Date: Feb 25, 2013 5:20 AM
Author: Brian M. Scott
Subject: Re: Problems with Infinity?

On Sun, 24 Feb 2013 22:23:25 -0800 (PST), "Ross A.Finlayson" <ross.finlayson@gmail.com> wrote in<news:c49c5ae4-834b-4791-a52e-35f9a7f6dbfa@h6g2000pbt.googlegroups.com>in rec.arts.sf.written,sci.math:> On Feb 24, 2:01 pm, Quadibloc <jsav...@ecn.ab.ca> wrote:>> On Feb 24, 12:00 am, Don Kuenz <garb...@crcomp.net> wrote:>>> Let's say a Mobius strip goes to infinity "feedback style" (in layman's>>> terms) while a line goes to two separate but equal infinities "linear>>> style." How many different infinities does that make according to>>> Cantor? One, two, or three?>> According to Cantor, the number of points on a line, or on a circle,>> has the cardinality of the continuum.>> The length of a line is aleph-null finite units of measure, on the>> other hand - and the length of a Mobius strip is finite, the distance>> it takes for you to get back where you started.>> Cantor's infinities, as was noted, aren't really about things like>> that.>> Basically, aleph-null is the first kind of infinity - the number of>> integers in the set {1, 2, 3, 4, 5, 6... }.>> It can be proven that one can pair off all the integers with that set:>> 1 <-> 0>> 2 <-> -1>> 3 <-> 1>> 4 <-> -2>> ...>> and so including the negative numbers doesn't really "double" that>> infinity. In fact, even the rational numbers can be paired off with>> the integers.>> Cantor's diagonal proof shows, though, that there are more *real>> numbers* than integers in a very real and unavoidable sense.>> http://www.quadibloc.com/math/infint.htm>> discusses the subject in more detail than I can do in a post.> Discussed the subject in somewhat more detail than a single post.> Arrange real numbers in a line this way.  For naturals n from 0 to d,> arrange n/d, in the order of the naturals.  As d (simply enough for> denominator) diverges to infinity, there are arrayed points between> zero and one, with a constant, infinitesimal difference from one to> the next, uniformly between zero and one.Good grief.  Is that crackpot still around?[...]Brian
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