Re: many (identical) universes

From: Fred Chen <flipsu5.domain.name.hidden>
Date: Mon, 14 Feb 2000 19:00:52 -0800

Selwyn St Leger wrote:

> > Date: Sun, 13 Feb 2000 12:58:59 -0800
> > From: Fred Chen <flipsu5.domain.name.hidden>
> > To: Saj Malhi <sajm.domain.name.hidden>
> > Cc: everything-list.domain.name.hidden
> > Subject: Re: many (identical) universes
>
> > Saj Malhi wrote:
>
> > > 2. The infinity of even numbers is as large as the infinity of all real
> > > numbers. Only different classes / types of infinity have been shown to be of
> > > different size.
> > >
> >
> > Hmmm...I would have thought the set of even numbers is much smaller than the set
> > of reals, because between any two even numbers, you have infinitely more reals.
> >
> > Fred
>
> Surely the even mumbers are a sub-set of the integers and thus of a
> lower order of infinity than the reals?
>
> Selwyn St Leger

My previous intuition would have led me to think that there are fewer evens than
integers, but more rigorously it seems possible to map evens to integers 1:1 by using
n->2n, and likewise for odds. However, it is difficult to imagine a way of doing this
for rationals (or reals).

I guess the issue for AUH would be: can we have meaningful probability with
infinities? Is the total number of evens 'half' the total number of integers, so that
any randomly picked integer has a 50% chance of being even? Perhaps instead of
discussing total number, we need number density.

Fred
Received on Mon Feb 14 2000 - 23:42:46 PST