Re: infinity

On 24 Aug 2005 08:23:13 -0700, "Jiri Lebl" <jirka@xxxxxx> wrote:

>*** T. Winter wrote:
>> As aleph_0 is (in the cardinal numbers) not divisible by any natural number,
>> it could be considered prime. Whether it is odd or even depends on your
>> definition. If you define a number even whenever it is divisible by 2,
>> aleph_0 is odd.
>
>I think this is taking it too far. The property of being prime, odd or
>even is a property of natural numbers, not of cardinal numbers
>(actually being prime is a property of a ring and the cardinal numbers
>are NOT a ring, they're not even a set).

I consider this an example of where the reliance on set theory has
hurt mathematics. Whether or not the objects form a set, is rather
peripheral to what a ring is. (How often do you actually use the set
part of the definition?)

Martin
.