Re: Review of Mueckenheims book.

In article <1172684786.688642.175760@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:


The identity function on omega is an automorphism of omega, a function
onto omega.

The word "automorphism" implies preservation of some algebraic structure
of the set other than mere membership, in which case, the nature of that
algebraic structure should be indicated.

Calling an identity function an "automorphism" in this context implies
what does not exist, and is Wm trying to pretend he knows some
mathematics.



If the identity function of every set exists, then the identity
function of P(omega) should exist too. But the different cardinality
of both functions, on omega and on P(omega) cannot be determined? It
must be a very artificial construction.

The identity function on any set is quite simple, it maps each element
of the set to itself:
f: S -> S : s |-> s, or
f(s) = s for every s in S.
.