[FOM] definition of the natural numbers

[Randall Holmes]

Dear List Members,

     I do actually know that the set of natural numbers can be defined
in ZF - Infinity (I received several pieces of private mail pointing this
out to me).  I didn't point this out because I was more concerned with
logical errors about the status of the definition in the post to which
I was responding, and also because the definition of the set of natural
numbers as the intersection of all inductive classes is the one that I
prefer (it works in NFU...).  My main point was that the standard definition
is meaningful in the absence of the axiom of infinity (it is not necessary
to have the axiom in order to understand it).  Of course it is not a good
definition to use in ZF - Infinity; in this I agree with the original poster
and everyone else :-)

                                         --Randall Holmes