
Re: Problems with Infinity?
Posted:
Feb 25, 2013 5:20 AM


On Sun, 24 Feb 2013 22:23:25 0800 (PST), "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote in <news:c49c5ae4834b4791a52e35f9a7f6dbfa@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 alephnull 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, alephnull 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

