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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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 Virgil Posts: 8,833 Registered: 1/6/11
Re: � 454 Equality and the axioms of natural numbers
Posted: Mar 22, 2014 4:57 AM

mueckenh@rz.fh-augsburg.de wrote:

> On Friday, 21 March 2014 20:51:41 UTC+1, Virgil wrote:
>
>

> >
> > 3. For every x in S, o =/= F(x)
> >
> > 4. For every x and y in S, if f(x) = f(y) then x = y

>
> How can the reader determine whether two numbers (or members) are equal or
> not equal. What is the definition of equality used here?

Identity, of course!
Since "x" and "y" and "f(x) and "f(y)" are merely names, x = y if and
only if "x" and "y" are merely different names for the same thing,
and f(x) = f(y) if and only if "f(x)" and "f(y)" are merely different
names for the same thing.

Thus, for example, one = ein and two = zwei
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