Date: Mar 22, 2014 4:57 AM
Subject: Re: � 454 Equality and the axioms of natural numbers
In article <email@example.com>,
> On Friday, 21 March 2014 20:51:41 UTC+1, Virgil wrote:
> > In article <firstname.lastname@example.org>,
> > 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