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Article 14873 of sci.space.shuttle:
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From: "Greg d. Moore" <mooregr@greenms.com>
Subject: Re: Stupid Math tricks  (was Re: Zeno's Paradox)
Message-ID: <3358552F.7ECA@greenms.com>
Date: Sat, 19 Apr 1997 01:16:31 -0400
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In article <3358EE52.270F@greenms.com>,
Greg d. Moore <mooregr@greenms.com> wrote:
>Ken Smith wrote:
>> 
>> In article <3358552F.7ECA@greenms.com>,
>> Greg d. Moore <mooregr@greenms.com> wrote:
>> 
>> >       No, but the explanation is rather simple.
>> 
>> Your argument is wrong.  There are more real values between 0 and 1 than
>> there are integers.
>> 
>
>	Umm, thanks for removing my comments.  Makes your point oh so much more
>clear. 
>
>	But that's what I said anyway.

Here's what you said:

>From: "Greg d. Moore" <mooregr@greenms.com>
>Subject: Re: Stupid Math tricks  (was Re: Zeno's Paradox)
>Message-ID: <3358552F.7ECA@greenms.com>
>Date: Sat, 19 Apr 1997 01:16:31 -0400
>Reply-To: mooregr@greenms.com
>Organization: Green Mountain Software
>X-Mailer: Mozilla 3.01 (WinNT; I)
>MIME-Version: 1.0
>Content-Type: text/plain; charset=us-ascii
>Content-Transfer-Encoding: 7bit
>Lines: 55

>jon murray wrote:
>> 
>> William Chops Westfield wrote:
>> >
>> >     Which is the larger set of numbers: All positive integers, or 
>> >all integers?
>> >     Both are infinity, but is one set twice as large as the other?
>> >
>> > They're the same size.  The set of all rational number (fractions) is
>> > the same size too.  But the set of irrational numbers is bigger...
>> >
>> > That should be obvious.
>> >
>> 
>> Well, not being a mathematitian, it isn't obvious to me. Is there any
>> imaginable situation where my lack of insight is likely to cause me a
>> problem?
>> 

>	No, but the explanation is rather simple.

>Integers 	1 -1 2 -2 3 -3 4 -4 etc... (This will obviously go to
>infinity)
>Positive Int	1  2 3  4 5  6 7  8 etc.  (This too will go to infinity).

>Basically you can count to infinity with either one.

>The reason irrationals are a "bigger" infinity is as follows.

>Count from 1 to 2 with every irrational inbetween...

>All Number set:   1 1.1 1.11 1.111 1.1111 1.11111 ...... up to 2.
>Integers	  1  2   3    4     5      6   up to infinity.

>So, (wrap your mind around this :-) you get to infinity with the
>integers before you get to 2.  So what happens when you finally get to
>2?  You're out of inifite integers, but you've got an inifity to go. :-)

>In other words, it takes an infinite number of "counters" to get from
>1.0 to 2.0.  So, it must take a BIGGER infinite number of counters to
>get from 1.0 to infinity.0.

>Make sense?

Proving that a subset is countibly infinite does not prove that the whole 
set must be uncountibly infinite.  If it did we could prove that there 
are no countibly infinite sets.


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