🚀 go-pugleaf

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.

> Proof:
> 
	Same idea, different approach.

> Imagine that you have an infinitely long page.  You could write down all
> of the integers from 0 to infinity on it.  If the number of real numbers
> was the same type of infinity as that of integers you could write down
> all of the numbers from 0.0 to 1.0 beside the integers.
> 
> Lets assume that you set out to do this and write all of the numbers in
> decimal form.  I would like to describe a new decimal number to you.
> Like all the others you have written it starts "0.".  The first digit
> after the decimal point will be determine by looking at the first digit
> after the decimal point in the first number on your list.  The second
> digit after the decimal point will be determined by the second digit
> after the decimal point in the second number on your list and so on.
> 
> In each case the digit in the digit in the new number will be 1 plus the
> digit from the list unless that digit is "9" in which case "0" will be
> used.  This new number is obviously a value between 0.0 and 1.0 because
> it starts out "0.".  It's first digit is different than the first digit
> of the first number on the list. Its second digit is different than the
> second digit of the second number on the list and so on.  This number
> therefor cannot be on the list so anny attempt to write the list of real
> numbers from 0.0 to 1.0 beside the list of integers can never contain all
> of the real numbers.
> 
> --
> --
> kensmith@rahul.net   forging knowledge

-- 
Greg D. Moore	President  	mooregr@greenms.com
Green Mountain Software		http://www.greenms.com/
518-273-8602