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Topic: § 454 Equality and the axioms of natural numbers
Replies: 30   Last Post: Mar 23, 2014 2:41 PM

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 Dan Christensen Posts: 7,660 Registered: 7/9/08
Re: § 454 Equality and the axioms of natural numb
ers

Posted: Mar 22, 2014 2:57 PM

On Friday, March 21, 2014 2:41:17 AM UTC-4, muec...@rz.fh-augsburg.de wrote:
> On Thursday, 20 March 2014 22:35:55 UTC+1, Dan Christensen wrote:
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> > The real numbers can also be constructed from Peano's axioms.
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> That was not the question.
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> > It should be
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> > possible to prove than no irrational number is equal to a natural number.
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> That was not the question.
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You wanted to know if it was possible to prove, starting from Peano's axioms, that pi (or any other irrational number?) is not equal to a natural number.

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> The question was: If the five truncated Peano axioms, not more and not less, define the natural numbers, as you said, what part of the axioms excluded that pi is a natural number?
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You are grasping at straws, WM. Again, the Peano axioms are just the 5 essential properties of the natural numbers from which it seems all others can be derived.

Dan