Dik T. Winter wrote:
In article .com "Schoenfeld" writes:
Dik T. Winter wrote:
...
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.

It is an additive identity by definition, the definition was for each x
there is y.

What is the additive identity in the addition table above? In what
way does the addition table above fail the requirement: "for all x
there exists y such that x + y = x"?

Your table has no relation to what I said. In fact, it doesn't even
have a relation to how additive identities are defined for
rings/groups/fields (another elementary error you've just made).

I'll repeat again, the AXIOM:
"Axiom: Additive Identity, for all x there exists y, x + y = x"

guarantees that an object 'y' exists for every single object 'x',
however the object 'y' is not an number.


Will you admit your error ?

When are you going to?

You have made the error, and in your attempt to cover it up, you have
made another error.


--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/