Virgil
Posts:
8,833
Registered:
1/6/11


Re: � 454 Equality and the axioms of natural numbers
Posted:
Mar 22, 2014 4:57 AM


In article <5ef18ee1a2f94ee1af9add2f296d5f0e@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Friday, 21 March 2014 20:51:41 UTC+1, Virgil wrote: > > In article <fe9e9fb1c93a430787da48cb1242957d@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 

