Re: Help in answering news story on refutation of fermat's last theorem


Torkel Franzen wrote:
> "Mark Nudelman" <markn@xxxxxxxxxxxxxxxxxxxxx> writes:
>
> > If the statement 0=1 is an axiom, then the symbols 0, 1, and =
cannot be
> > interpreted as they are in normal arithmetic.
>
> Sure they can. 0=1 simply becomes a false axiom.

What is a false axiom?

> > Symbols can't
> > be interpreted unless you know how they're used in the axiomatic
system
> > which they're part of.
>
> So what axiomatic system are the symbols in your statement above a
> part of?

You can pick any axiomatic system you want. In some the statement 0=1
will be true. In others - false.

As the previous poster told you, take the usual axioms of integers,
including inductive ordering, and let the symbol "=" denote what we
usually denote as "<". Then "0=1" is a correct statement.

.