Quote Originally Posted by Kantian Pragmatist View Post
Why does 5+5=10? This might seem a stupid question to any that can count, obviously 5+5=10, but tell me, what is it about these things that make this so. Whether you are Christian or Islamic, Mayan or Pygmy, if you answer 9 or 15 or any other number but 10 to this question, you would be wrong. There is something fundamentally beyond mere human agreement that makes 5+5=10. In a sense, it is rather like the truth that something is there when you stub your toe in the dark. You can keep kicking whatever it is in your way, it's not going to magically disappear because you want it to. Likewise, you can wish all you want that 5+5=anything else, but that's not going to make it so.
Actually, mathematically proving that 1+1=2 is very hard, or so I have been told.
Some things might seem obvious, but that doesn't mean anything.
The square root of -1 doesn't logically exist, but if we just pretend it doesn, then a whole lot of things like frequency response analysis of transmission lines and amplifiers becomes a whole lot easier.

Likewise, division by zero gives meaningless results, but in some cases we can still extract meaningful results if we fudge the division away.
And I read last year that one mathematician had found a way -in some cases- to handle the division by zero by pretending it gives a result (just like with sqrt (-1)).

So it is anything but obvious that 5+5=10. It might seem obvious, but so do a lot of other things.
And 5+5 is only 10 in an assumed field of numbers that is infinite. If 8 is the highest number in a system, then 5+5 is either meaningless, or perhaps the boundary violation crosses back into itself and 5+5=2

I am not a mathematician (I do have a Masters Degree in Engineering), so I can only describe it in layman's terms. Jimbo could explain it much better, but the fundamental idea is correct.
Saying that 5+5 is always 10 is plain wrong. Even in our universe, there are things which are described using math that is based on different assumptions, even if only because that is the easiest way to prove theories and produce results.