1. RE: [OT] How many integers?
Igor Kachan wrote:
> I say, Russian is better for such the things 
> We say "power of a set", not "size of a set".
If I were being correct, I really should have said the "cardinality of
the set." To my [native speaking american-english] ear, "size" sounds
better than "power". (Plus my "proof" actually contains a lot of hand
waving that might not be clear to someone not familiar with set theory.)
...and then Igor wrote:
> Then, Russians say "multitude" or "host", not "set".
> So, "power of the normal integers host" forces to think
> about infinity first of all.
> And "host" itself may be small - as "set" is something
> small first of all.
"Power of the normal integers host" sounds like you're talking about an
army or something to me. :) Then again, the "power of the host" of
Russian words I know is a very small number.
> Russian is good for such the things, isn't it? 
Well, I've heard that you guys have some pretty sharp mathematicians, so
I won't disagree with you (though IMHO it was a Frenchman who was
probably the greatest pioneer in this area--Cauchy--so I wonder what the
French would say?). Guess it's another case of imperfect translations.
I still like english, BTW. :p
Matt Lewis
2. RE: [OT] How many integers?
> From: Igor Kachan [mailto:kinz at peterlink.ru]
> > Well, I've heard that you guys have some pretty sharp
> > mathematicians, so I won't disagree with you
> > (though IMHO it was a Frenchman who was probably the
> > greatest pioneer in this area--Cauchy--so I wonder
> > what the French would say?).
>
> This is a German source, Cantor's theory,
> he was the first setman-hostman-multitudeman
<blush> You're correct. Not sure what I was thinking (must have gotten a
Cauchy Sequence confused with a Cantor Set). Although I believe his parents
were Danish, he lived in Russia for a while before moving to Frankfurt (he
also spent a year at the University of Zurich).
Matt Lewis
3. RE: [OT] How many integers?
- Posted by rforno at tutopia.com
Jun 11, 2003
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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