Re: Cantor's diagonal proof wrong?

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 11/22/04 

Date: Mon, 22 Nov 2004 00:37:32 -0500

In <20041118145224.702$3i@newsreader.com>, on 11/18/2004
   at 07:52 PM, curt@kcwc.com (Curt Welch) said:

>We are trained like parrots to say ".2 is a number".

No. We are trained to understand what a number is, and to understand
that '.2'10, 1/5 and '.1'5 are all names for the same number, and why.

>And, because I seem not to be following my training,

No, because what you are saying is nonsense.

>Counting is a procedure.

Counting is not a number.

>I'm not saying it is wrong to call 1/5 a number. I'm saying that
>behind those words is a hidden procedure

Saying so doesn't make it true.

>..2 represents the results of dividing 1 by 5.

It also represents the result of dividing 4 by 20. Which of those
procedures is the real .2?

>The addition procedure is multiple applications of the
>counting procedure.

Please explicate the "procedure" for Pi+e.

>In the above problem, there is no counting number which we can find
>to multiply 5 by in order to produce one. So we invent a new
>notation called decimal numbers

No. We were doing fractions long before the invention of decimal
notation. 

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Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
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