# Re: Rationals vs Reals in Comp

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On 23 Apr 2013, at 21:29, Brian Tenneson wrote:```
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```Interesting read.

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The problem I have with this is that in set theory, there are several examples of sets who owe their existence to axioms alone. In other words, there is an axiom that states there is a set X such that (blah, blah, blah). How are we to know which sets/notions are meaningless concepts? Because to me, it sounds like Doron's personal opinion that some concepts are meaningless while other concepts like huge, unknowable, and tiny are not meaningless. Is there anything that would remove the opinion portion of this?
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How is the second axiom an improvement while containing words like huge, unknowable, and tiny??
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So I deny even the existence of the Peano axiom that every integer has a successor.
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I guess the author means that he denies the truth of the axiom of the Peano axiom.
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```Eventually
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we would get an overflow error in the big computer in the sky, and the sum and product of any two integers is well-defined only if the result is less than p, or if one wishes, one can compute them modulo p. Since p is so large, this is not a practical problem, since the overflow in our earthly computers comes so much sooner than the overflow errors in the big computer in the sky.
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What if the big computer in the sky is infinite?
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Indeed.

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Or if all computers are finite in capacity yet there is no largest computer?
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Indeed.

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What if NO computer activity is relevant to the set of numbers that exist "mathematically"?
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Indeed.

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Eventually it depends on the theory we start from. But to start the reasoning in comp, we have to assume at least one universal system (in the Church-Turing sense). If not, we don't get it. It remains a logical possibility of using some physicalist ultrafinitism, but this is heavy to only drop an explanation of the origin of consciousness/ physical--realities coupling. And by MGA + occam, unless there is flaw, this cannot work with comp.
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Bruno

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On Monday, April 22, 2013 11:28:46 AM UTC-7, smi...@zonnet.nl wrote:
See here:

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf

Saibal

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