|
|
> Lefty wrote:
> Snip >you can easily say
> > that 1 = 7-6 = 10-9, etc etc, and that these separate things are
> > identical because it can be proven - snip
>
> But you would be wrong. The 1 is an integer, whilst 6,7,9 & 10 are
> natural numbers; the symbol "-" is an ill defined conflation of two
> concepts (negate & subtract). The correct statement is an equivalence
> relationship 1 ~ {7,6} ~{10,9} (van der Waerden, Algebra, 1970,
> Springer reprint 2003). Negation is an axiom (Axiom 4a, Allenby, Rings,
> Fields & Groups, Blackie 1971) and other axioms give other algebras.
> Subtraction is a difficult concept (Smith & Romanskaya, Post Modern
> Algebra p111).
I think that you know what I meant. 1=1. Very simple. 2=2. 10=10. x=x, y=y,
and z=z.
But lets try this with physical objects. (10 Chevy trucks) = (10 Toyota
trucks). Hmmmmm. maybe there's a problem here.
OK, I have 10 Chevy trucks and you also have 10 Chevy trucks. My (10 Chevy
trucks) = Your (10 Chevy trucks). Are they equal ? Equivalent ? Same ?
Probably not. Mine need an oil change, and yours are rusty.
The process of counting is a MODEL of reality, and does not match reality
precisely.
No two "physical" objects can EVER be identical. Certainly not the way that
abstract objects can.
|
|