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Topic: AN ERROR IN PEANO ARITHMETIC! x X [ s Y ] [ + X Z ] <- x X Y Z
Replies: 3   Last Post: Nov 5, 2013 10:21 PM

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Graham Cooper

Posts: 4,253
Registered: 5/20/10
Re: AN ERROR IN PEANO ARITHMETIC! x X [ s Y ] [ + X Z ] <- x X
Y Z

Posted: Nov 5, 2013 10:21 PM
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On Tuesday, November 5, 2013 2:24:21 PM UTC-8, Ben Bacarisse wrote:
> grahamcooper7@gmail.com writes:
>
> That's too general, in my opinion. You need a funny representation that
>
> makes the question rather debatable -- one could argue that the
>
> representation has done most of the work of the addition.
>



OK, if FSMs could do Logs then maybe you'd have a reasonable objection.

Formally it's just a derivation, the impossible proof by contradiction is
after the representation is decided, AFAIK.

But it's a strong result, formally you cannot even say ADDITION and
MULTIPLICATION... substitute the term ADDITION for "ADDITION AS WE KNOW IT"
and the proof holds bona fide!


Herc




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