In article . com "Schoenfeld" writes:
Dik T. Winter wrote:
....
Axiom: Additive Identity
for all x there exists y such that x + y = x
guarantees an additive identity.

Nope. The axiom is "there is an y such that for all x: x + y = x".
Something slightly different.

Is that your way of dodging an error you made but tacticly did not
explicitly write?

The statement,
Axiom: Additive Identity
"for all x there exists y such that x + y = x"
defines an additive identity for all x.

No it does not. Consider the following addition table:
+ a b c
a a c b
b c b a
c b a c

For each 'x' there is an 'y' such that 'x + y = x'. But there is not
an additive identity.

Your error was assuming that no such y existed because no such number
exists, but to get numbers you need a ring and the axiom above is not
compatable with that of a ring.

I am assuming nothing about numbers at all. I only look at the axiom
and sees that it does not define an additive identity.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/