Quote by cheesemonkey
But what I'm saying is that in my system, 0 doesn't necessarily equal 1, because that is a statement that was derived from my system by multiplying both sides by 0, thus potentially changing the system's truth value; therefore, it may very well be the case that 1/0=1/0 never was a false statement (it just turned into one when we multiplied both sides by 0).

Why don't you just define the system for us? That way we can comment on it directly, rather than making statements like "0
doesn't necessarily equal 1".