Re: Idle Thoughts

On 22 Aug 2005 19:18:23 -0700, "Nick Hodges [TeamB]"
<nickhodges@xxxxxxxxx> wrote:

>> It' along
>> the lines of "Infinity + 1 = Infinity"
>
>Indeed -- which, of course, proves that 1=0.

Infinity is strange :)

Cantor's basic definition was "a collection is infinite, if some of
its parts are as big as the whole".

Take the set of natural numbers N = {1, 2, 3, ....}, which is
infinitely large. Now consider the set of even (natural) numbers {2,
4, 6, ....}. "Obviously" there must be twice as many natural numbers
as even numbers.

However, for each number n in N, you can create the even number 2n.
Since you can do this for each and every number in N, we see that the
two sets have the same size.

Infinity is strange :)

- Asbjørn
.

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