Once again, logic flaws
Quote:Based in the context of my original theory the mathematical property of the String (being of an undefined length) and the mathematical property of infinity (being of an undefined value) hold enough similarities, that I would say that you could define the lenght of a piece of string infinately long.
The equations a = c and b = c then a=b prove this point, (if a b and c are all either undefined lengths of string or infinity) the equations do not work (as you have shown) with finite values : $1 = money, $1,000,000 = money, therefore $1 = $1,000,000. This highlights the limitiation of the equations rather than the limitation of my theory.
You are talking about logic, not equations. Logic handles your supposition fine. A does not equal B, it implies B. In mathmatics, "equal" means one-to-one correspondance. "Implies" connotates "is a subset of". Cat does not equal animal, cat implies animal. Animal includes cat, but a member of the animal family does not have to be a cat. It's not an equal sign, it's a one way arrow. Likewise, dog implies animal, but we all know that dog is not cat.
There are rules for logic that make for good fun and lots of neat terms like inverse, converse and my favorite, contrapositive.