🚀 go-pugleaf

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.

Proof:

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.


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