Re: What is this thing known as "=" ?


T.H. Ray wrote:
T.H. Ray wrote:

> that someone else wrote:

There are different kinds of "equal". Which kind
are
you talking about?

Nonsense. Equivalence, in a mathematical equation,
has only one meaning. I have recited it for you.
Whatever else you want to say about equivalence may
have some personal meaning to you, but it has
nothing to
to do with mathematics.

Ah, you think that identity is trivial?

http://hdebruijn.soo.dto.tudelft.nl/fototjes/gezocht.h
tm

Han de Bruijn


Do you think that every equation is an identity
equation?

Tom


Tom, I still think that I'm miscommunicating what I'm going after in
this.

Look at this proof again,
http://en.wikipedia.org/wiki/Zero_element

--------------------------------------------------------
Proving the uniqueness of a zero element is equivalent to proving the
uniqueness of an additive identity. Assuming there are two, 0 and 0',
we have that 0 = 0 + 0' = 0', so that 0 must be unique. Thus we can
speak of the zero element in a system.
--------------------------------------------------------

OK - they are saying that since 0 = 0', hence 0 must be unique because
0 _is_ 0'.

Simply showing that zero is quantitatively equal to zero' does not
prove uniqueness in my opinion. Unless you are suggesting that quantity
is a property which is inherently endowed with uniqueness - maybe
that's the case. Then, quantitative equivalence would imply that 0 "is"
0' and the proof would establish uniqueness, but that entails a pretty
substantial assumption that you have already proved the uniqueness of
the reals, in which case uniqueness of zero is implied anyway. I dont
like this usage of " = ".

.

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