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Topic: Problems with Infinity?
Replies: 72   Last Post: Apr 12, 2013 1:36 PM

 Messages: [ Previous | Next ]
 Brian M. Scott Posts: 1,289 Registered: 12/6/04
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
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.

>> 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

Date Subject Author
2/24/13 William Elliot
2/24/13 garabik-news-2005-05@kassiopeia.juls.savba.sk
2/24/13 Frederick Williams
2/24/13 David DeLaney
2/25/13 P. Taine
2/26/13 Butch Malahide
2/24/13 jsavard@ecn.ab.ca
2/25/13 ross.finlayson@gmail.com
2/25/13 Brian M. Scott
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 jsavard@ecn.ab.ca
2/25/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/26/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/25/13 Frederick Williams
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/27/13 David DeLaney
2/27/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
2/28/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
3/1/13 Shmuel (Seymour J.) Metz
3/1/13 David DeLaney
3/2/13 Shmuel (Seymour J.) Metz
2/28/13 jsavard@ecn.ab.ca
2/28/13 David Johnston
2/27/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/26/13 David DeLaney
4/11/13 Walter Bushell
4/11/13 Brian M. Scott
4/11/13 Butch Malahide
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/11/13 jsavard@ecn.ab.ca
4/11/13 Butch Malahide
4/12/13 Virgil
4/12/13 Brian M. Scott
4/12/13 jsavard@ecn.ab.ca
4/11/13 fom
4/11/13 Butch Malahide
4/11/13 Butch Malahide
4/12/13 Brian M. Scott
4/12/13 Butch Malahide
2/26/13 Brian M. Scott
2/26/13 Shmuel (Seymour J.) Metz
2/26/13 Brian M. Scott
2/26/13 David Bernier
2/26/13 Shmuel (Seymour J.) Metz
2/28/13 Shmuel (Seymour J.) Metz
4/11/13 Walter Bushell
4/11/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/27/13 Scott Fluhrer