Re: Ultimate debunking of Cantor's Theory

On Sat, 14 Jul 2007 13:55:46 +0000 (UTC), stephen@xxxxxxxxxx wrote:


[...] A list and a set are rather different beasts.
A list can contain the same element any number
of times.

( 1, 1, 1, 1, 1, 1, 1, 1, 1, ... )

is a perfectly fine infinite list.
A list is simply a function from N to whatever set of objects
you are listing. A function is simply a set of ordered pairs.
The above lists typical representation as a set would be

{ {0,1}, {1,1}, {2,1}, {3,1}, {4,1}, {5,1}, ... }

Or rather:

{ (0,1), (1,1), (2,1), (3,1), (4,1), (5,1), ... }.

;-)

oops. :)

How about

{ {0,{0,1}}, {1,{1}}, {2,{1,2}}, {3,{1,3}}, {4,{1,4}}, {5,{1,5}}, ... }

? :)

I'd personally prefer


{{{0},{0,1}}, {{1}}, {{2},{1,2}}, {{3},{1,3}}, {{4},{1,4}},
{{5},{1,5}}, ... }.


F.

--

E-mail: info<at>simple-line<dot>de
.

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