Schoenfeld wrote:
Robert Low wrote:
So any two objects which have the defining property
of an additive identity must be equal. Or, to put
that in plainer language, the additive identity
is unique.
I realize that now. Unfortunately I was thinking
"for all x there exists y such that x + y = x" which doesn't guarantee
uniqueness at all.

Indeed, it doesn't even guarantee the existence of an
additive identity. Yep, there's nothing to beat understanding
the things you're trying to talk about.