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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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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: § 454 Equality and the axioms of natural numb
ers

Posted: Mar 21, 2014 2:44 AM

On Friday, 21 March 2014 01:08:38 UTC+1, Virgil wrote:
>
> "Dan Christensen" <Dan_Christensen@sympatico.ca> wrote:
>
>
>

> > Then let us know whether pi is a natural number - from the Peano axioms
>
> > which, according to you, "fully capture the common intuition of the natural
>
> > numbers".
>
>
>
> First give us your definition of pi.

It is the circumference of an ideal circle divided by its diameter.
You can also understand the area of this circle divided by it radius^2 as pi.
>
>
>
> I suspect that your definition will clash with the Peano axioms using
> either 0 or 1 as the non-successor natural and x + 1 as successor of x

That is obviuos. But the modern logicians do not know what +1 means.
Although they know what being equal means for natural numbers, namely containing as many units.

Regards, WM