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Topic: ALL PERMUTATIONS OF INFINITY
Replies: 156   Last Post: Jun 28, 2012 9:34 PM

 Messages: [ Previous | Next ]
 Torben Mogensen Posts: 60 Registered: 12/6/04
Re: ALL PERMUTATIONS OF INFINITY
Posted: May 21, 2012 12:46 PM

Graham Cooper <grahamcooper7@gmail.com> writes:

> How many ways can you re-order <f, a, t> ?
> <f a t>
> <f t a>
> <a f t>
> <a t f>
> <t f a>
> <t a f>
>
> 3! = 3 Factorial = 3X2X1 = 6
>
> How many different ways can you order <1,2,3,4....> ?
>
> oo X oo-1 X oo-2 X .... X 3 X 2 X 1
> It's not well defined!

Not if you write it like this, but the number of permutations of a set
is well defined even for infinite sets -- just like the number of all
subsets of a set is defined even for infinite sets.

For finite and infinite sets, two sets are considered to have the same
number of elements if there exists a bijection between them. For
example, the set of even naturals has the same size as the set of all
naturals (N), because f(n)=2*n is a bijection between naturals and even
naturals. For the same reason, the set of all sets of naturals (P(N)
or, equivalently, 2^N) has the same size as the set of real numbers (R):
There is a bijection between sets of naturals and reals.

There is a bijection between permutations of N and subsets of N, so the
set of permutations has the same size as the set of subsets.

Torben

Date Subject Author
5/20/12 Graham Cooper
5/20/12 K_h
5/20/12 Graham Cooper
5/21/12 Torben Mogensen
5/21/12 Graham Cooper
5/21/12 Graham Cooper
5/22/12 mueckenh@rz.fh-augsburg.de
5/22/12 Graham Cooper
5/22/12 Graham Cooper
5/23/12 mueckenh@rz.fh-augsburg.de
5/23/12 donstockbauer@hotmail.com
5/24/12 Uirgil
5/24/12 Graham Cooper
5/22/12 Graham Cooper
5/22/12 Uirgil
5/23/12 mueckenh@rz.fh-augsburg.de
5/24/12 Uirgil
5/24/12 mueckenh@rz.fh-augsburg.de
5/24/12 Curt Welch
5/24/12 mueckenh@rz.fh-augsburg.de
5/24/12 Curt Welch
5/24/12 Graham Cooper
5/24/12 Curt Welch
5/24/12 Graham Cooper
5/24/12 mueckenh@rz.fh-augsburg.de
5/24/12 Curt Welch
5/25/12 Uirgil
5/25/12 Curt Welch
5/26/12 K_h
5/27/12 Curt Welch
5/27/12 Uergil
5/27/12 Curt Welch
5/27/12 ross.finlayson@gmail.com
5/27/12 K_h
5/27/12 Graham Cooper
5/27/12 Graham Cooper
5/27/12 Curt Welch
5/27/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 K_h
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 donstockbauer@hotmail.com
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/29/12 Owen Jacobson
5/27/12 K_h
5/27/12 David Bernier
5/27/12 Androcles
5/27/12 Curt Welch
5/28/12 K_h
5/28/12 Curt Welch
5/27/12 Shmuel (Seymour J.) Metz
5/25/12 Shmuel (Seymour J.) Metz
5/25/12 mueckenh@rz.fh-augsburg.de
5/25/12 Uirgil
5/26/12 mueckenh@rz.fh-augsburg.de
5/26/12 Uirgil
5/26/12 Curt Welch
5/27/12 Shmuel (Seymour J.) Metz
6/28/12
5/29/12 Owen Jacobson
5/29/12 Graham Cooper
5/25/12 Graham Cooper
5/26/12 Curt Welch
5/27/12 Shmuel (Seymour J.) Metz
5/29/12 Ralph Hartley
5/29/12 Curt Welch
5/24/12 Uirgil
5/24/12 Shmuel (Seymour J.) Metz
5/24/12 mueckenh@rz.fh-augsburg.de
5/24/12 Graham Cooper
5/24/12 Curt Welch
5/24/12 Graham Cooper
5/25/12 Shmuel (Seymour J.) Metz
5/25/12 mueckenh@rz.fh-augsburg.de
5/25/12 Uirgil
5/26/12 Curt Welch
5/27/12 Shmuel (Seymour J.) Metz
5/27/12 Curt Welch
5/27/12 Graham Cooper
5/27/12 Curt Welch
5/25/12 Uirgil
5/24/12 Curt Welch
5/24/12 Graham Cooper
5/24/12 Graham Cooper
5/25/12 Curt Welch
5/25/12 Curt Welch
5/25/12 Graham Cooper
5/26/12 Curt Welch
5/26/12 Graham Cooper
5/27/12 Shmuel (Seymour J.) Metz
5/25/12 Shmuel (Seymour J.) Metz
5/25/12 K_h
5/25/12 mueckenh@rz.fh-augsburg.de
5/25/12 Uirgil
5/26/12 Curt Welch
5/26/12 Graham Cooper
5/26/12 K_h
5/24/12 LudovicoVan
5/25/12 K_h
5/25/12 mueckenh@rz.fh-augsburg.de
5/25/12 Shmuel (Seymour J.) Metz
5/26/12 Curt Welch
5/26/12 K_h
5/27/12 Curt Welch
5/27/12 Uergil
5/27/12 mueckenh@rz.fh-augsburg.de
5/27/12 Uergil
5/27/12 K_h
5/27/12 Graham Cooper
5/27/12 Curt Welch
5/28/12 K_h
5/28/12 Curt Welch
5/30/12 K_h
5/27/12 Shmuel (Seymour J.) Metz
5/25/12 netzweltler
5/26/12 Curt Welch
5/27/12 Shmuel (Seymour J.) Metz
5/28/12 netzweltler
5/28/12 ross.finlayson@gmail.com
5/28/12 Uergil
5/29/12 netzweltler
5/29/12 Curt Welch
5/29/12 netzweltler
5/29/12 Curt Welch
5/29/12 netzweltler
5/29/12 Curt Welch
5/30/12 netzweltler
5/29/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Graham Cooper
5/28/12 Curt Welch
5/28/12 Wally W.
5/28/12 donstockbauer@hotmail.com
5/28/12 |-| E R C
5/29/12 Curt Welch
5/30/12 Wally W.
5/30/12 Curt Welch
6/2/12 K_h
6/2/12 |-| E R C
5/24/12 Uirgil
5/24/12 LudovicoVan
5/24/12 Uirgil