OpenEuphoria

RE: [OT] How many integers?

• Posted by rforno at tutopia.com Jun 11, 2003
• 383 views

That's true, but one of the paradoxes of infinity is that, once you
eliminate even numbers from the set of all integers, it still remains an
infinity of numbers, the odd ones. What I was trying to do is answering the
original issue, that questioned that an infinite could be greater than
another one. So, inf1 = inf2 is as good as inf1 < inf2 or inf1 > inf2.... or
at least I think so ;).
For example, lim [x->infinite] (2 * x / x) equals 2, and as computer
arithmetic doesn't know how each infinite was obtained, any result should be
admissible from subtracting, dividing, etc, the computer representation of
infinite quantities. The original issue was that inf - inf should not return
inf.
Regards.
----- Original Message -----
From: Matt Lewis <matthewwalkerlewis at yahoo.com>
To: EUforum <EUforum at topica.com>
Sent: Monday, June 09, 2003 7:31 AM
Subject: [OT] How many integers?


>
>
> rforno at tutopia.com wrote:
> > You know, the set of *all* integers (abstract integers, not
> > Euphoria nor C nor computer integers) is infinite, but larger than
> > the set of *even* integers, that is also infinite.
>
> Actually, the set of even integers (let's call it ZE) and the set of all
> integers (Z) are the same size (countably infinite).  The standard way
> to prove this is to use some function to map from one set to the other,
> showing that there is the sets map each other completely with a
> one-to-one relationship  (bijective):
>
> Then for any z in Z, there is a ze in ZE such that z = ze / 2.  In other
> words, for any normal integer, I can use even integers to 'count' the
> normal integers, and so the sets must be the same size (btw, the set of
> rational numbers is the same size, but any interval of real numbers will
> be bigger).
>
> Matt Lewis
>
>
>
> TOPICA - Start your own email discussion group. FREE!
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>