On 24 Apr 2013, at 23:54, smi...@zonnet.nl wrote:

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Perhaps one should define things such that it can be impolemented byany arbitrary finite state machine, no mater how large. Then, whilethere may not be a limit to the capacity of finite state machines,each such machine has a finite capacity, and therefore in none ofthese machines can one implement the Peano axiom that every integerhas a successor.

Number(0) Number(s(x)) := Number(x)

`This implements (in PROLOG) the Peano axiom that every number has a`

`successor`

`What you say is that the existential query "Number(x)?" will lead the`

`PROLOG machine into a non terminating computation. It will generates`

`0, s(0), s(s(0)), s(s(s(0))), s(s(s(s(0)))), ....`

`Similarly, you can implement a universal machine in a finite code. But`

`then the machine will ask sometimes for more memory space, like us.`

But some other properties of integers are valid if they are valid inevery finite state machine that implement arithmetic modulo primenumbers.

`Not the fundamental recursion properties. If you fix the prime number,`

`you will stay in an ultrafinistic setting, without recursion, without`

`universal machine, without any fertile theorems of computer science`

`which makes sense even if it means that the machines, when implemented`

`in a limited environment will complain, write on the walls, or will`

`build a rocket to explore space and expand their memory by themselves.`

I'm not into the foundations of math, I'll leave that to Bruno :) .But since we are machines with a finite brain capacity,

`In the long run, it is a growing one. And we have infinite capacities`

`relatively to our neighborhood. We don't stop to expand ourselves.`

and even the entire visible universe has only a finite informationcontent,

`If the physical universe is finite, but very big, we are still`

`universal machine. But doomed for some long run. No worry if comp is`

`true, as comp precludes a finite physical universe.`

we should be able to replace real analysis with discrete analysis asexplained by Doron.

`That can makes sense for some application, but would contradict comp`

`for the theoretical consequences.`

Bruno

Saibal Citeren Brian Tenneson <tenn...@gmail.com>:Interesting read. The problem I have with this is that in set theory, there are severalexamples of sets who owe their existence to axioms alone. In otherwords,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 meaninglessconcepts?Because to me, it sounds like Doron's personal opinion that someconceptsare meaningless while other concepts like huge, unknowable, andtiny arenot meaningless. Is there anything that would remove the opinionportionof this?How is the second axiom an improvement while containing words likehuge,unknowable, and tiny?? quoteSo I deny even the existence of the Peano axiom that every integerhas asuccessor. Eventuallywe would get an overflow error in the big computer in the sky, andthe sumand product of anytwo integers is well-defined only if the result is less than p, orif onewishes, one can compute themmodulo p. Since p is so large, this is not a practical problem,since theoverflow in our earthlycomputers comes so much sooner than the overflow errors in the bigcomputerin the sky. end quoteWhat if the big computer in the sky is infinite? Or if allcomputers arefinite in capacity yet there is no largest computer?What if NO computer activity is relevant to the set of numbers thatexist"mathematically"? 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> To post to this group, send email toeveryth...@googlegroups.com<javascript:>.> Visit this group at http://groups.google.com/group/everything-list?hl=en.> For more options, visit https://groups.google.com/groups/opt_out. > > >--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-l...@googlegroups.com.Visit this group at http://groups.google.com/group/everything-list?hl=en.For more options, visit https://groups.google.com/groups/opt_out.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com.Visit this group at http://groups.google.com/group/everything-list?hl=en.For more options, visit https://groups.google.com/groups/opt_out.

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