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

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jsavard@ecn.ab.ca

Posts: 318
Registered: 12/12/04
Re: Problems with Infinity?
Posted: Feb 24, 2013 5:01 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

John Savard



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

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