Re: Can ZFC prove Addition is Associative?

Norman Megill wrote:
In the quotation above from my web page,
http://us.metamath.org/mpegif/mmset.html#staxioms, the phrase "the
axioms" means _all_ of the preceding axioms, which include prop.
calc., pred. calc., and ZFC axioms, _not_ just the 7 preceding ZFC
axioms. In addition, there is an important note following it that
clarifies and re-emphasizes this, specifically intended to prevent
this exact kind of misunderstanding, which was apparently overlooked.
In full context, the quotation reads:

There you have it, the axioms for (essentially) all of
mathematics! ... If you keep a copy in your wallet, you will
carry with you the encoding for all theorems ever proved and that
ever will be proved, from the most mundane to the most profound.

Note. Books often make statements like "(essentially) all of
mathematics can be derived from the ZFC axioms." This should not
be taken literally-there's not much you can do with those 7 axioms
by themselves! Implicitly the authors mean the ZFC axioms plus
the axioms and rules of propositional and predicate calculus,
which total 22 axioms and 2 rules in our system. Together these
constitute what is called "ZFC set theory."

I though it was clear, but I may try to rewrite it to be clearer, if
it is
still causing confusion.

Seems clear to me.

--
David Marcus
.

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