`Perhaps one should define things such that it can be impolemented by`

`any arbitrary finite state machine, no mater how large. Then, while`

`there may not be a limit to the capacity of finite state machines, each`

`such machine has a finite capacity, and therefore in none of these`

`machines can one implement the Peano axiom that every integer has a`

`successor. But some other properties of integers are valid if they are`

`valid in every finite state machine that implement arithmetic modulo`

`prime numbers.`

`I'm not into the foundations of math, I'll leave that to Bruno :) . But`

`since we are machines with a finite brain capacity, and even the entire`

`visible universe has only a finite information content, we should be`

`able to replace real analysis with discrete analysis as explained by`

`Doron.`

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Saibal Citeren Brian Tenneson <tenn...@gmail.com>:

Interesting read. 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? How is the second axiom an improvement while containing words like huge, unknowable, and tiny?? quote So I deny even the existence of the Peano axiom that every integer has a successor. Eventually 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. end quote What if the big computer in the sky is infinite? Or if all computers are finite in capacity yet there is no largest computer? What if NO computer activity is relevant to the set of numbers that exist "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-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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