"Schoenfeld" writes:

David Kastrup wrote:
"Schoenfeld" writes:

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"

You got quantifier dyslexia, right?

You're as useless as rubber lips on a wood pecker.

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

The word "number" as you use it is meaningless. Anyway, additive
identities are not something dependent on x. You got your quantifiers
wrong.

You're two letters off from being an asset to this thread.

If you were able to read a simple table, you'd notice the
difference.

A guy with your IQ should have a low voice too.

Oh, I have. When I am not singing alto in my choir for stylistic
reasons, I am singing bass. Easier on the voice than tenor. One
should just realize when shouting from the chest does not help in
making a particular approach go the distance.

Anyway, we all feel honored for you offering those pearls of wisdom
which your teachers must never have tired of telling you. You could
try calling your axiom something differently than "additive identity"
since that name is already taken, maybe something like "indifferent
companion". On the other hand, changing the name might make your
attempt to bluff your way out of the hole you are digging for yourself
more apparent on other fronts.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum