I disagree the difference is so clear to most. In fact, I imagine most believe themselves to be of a privileged status, smarter than everyone else and definitively hating groups like ours. Mostly this hate stems from an ignorance of what we are all about. In the end the shape of the earth isn't the most important ideal we hold, or even in the long run an ideal that matters. Generally, if something that exists pisses the shit out of you, its likely worth examining a few times more. Question EVERYTHING.
mathsman, I'm familiar with why you say I'm wrong, but I'm demonstrating a concept that shows the arbitrary decision making in the mathematical academic and arm chair world. Some things in math are simply done out of convention and out of interest. In fact one can say all things done in math are done out of convention or interest. Surely that could be said for most peoples lives. For example, take conventions concerning division by zero.
The fact that we math is a word game is not an argument made to circle. It is self evident; when not so, definition of terms must be necessary to ensure even communication.
Prostitution is surely a game. Its hardly a game of words. Math is literally communicated via language comprised of words that can be assembled in order determined by rules of syntax and convention. To try to say one cannot examine the opposite cases or alternate cases from defined convention is to blindly have faith in said conventions and to have never learned anything for oneself, instead content to be fed from a silver spoon.
The point in all this is, if I wanted to define 1+1 = 3, I am more than welcome to. The math police isn't going to break down my door and write me a ticket. No one of any sense would bother.