Date: Mar 22, 2014 4:57 AM
Author: Virgil
Subject: Re: � 454 Equality and the axioms of natural numbers
In article <5ef18ee1-a2f9-4ee1-af9a-dd2f296d5f0e@googlegroups.com>,

mueckenh@rz.fh-augsburg.de wrote:

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

> > In article <fe9e9fb1-c93a-4307-87da-48cb1242957d@googlegroups.com>,

>

>

> >

> > 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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