But in reality, if I have 5 apples, you can only take 5 apples. Not six and therefore leave me with -1 apple. See what I mean

Yeah, but this is just an application of numbers, it's not where the numbers themselves come from.

Yes, we started out by physical counting with examples like that, but then we realised that we didn't just invent a counting system, we'd discovered a deep system of logic, and we now call your "non-imagined" set of numbers the "natural numbers".

Also, the fact that you count the apples in multiples of "1" is just a convention. If we used a strange convention where we do everything the opposite way around, we can still count. I can say each apple is worth "-1" (

*and -1 + -1 + -1 + -1 + -1 == -5, so*) you've got "-5" apples in this bizarro convention, and I take 4 of them (and taking an apple is worth "+1"), then "-5 + 4" leaves you with "-1" apple, which equates to 1 apple in the regular convention.

If you think of mass as just being another "named attribute" that a point can have, and charge is another "named attribute", then it's not so weird -- electricity is a flow of particles with negative charges. But we could just as well have called them "positive charges" or "up charges" or "strange charges", if different people had done the naming.

Or if you think of positive mass as something that sucks space-time in towards it (

*like a vacuum cleaner's nozzle against a bed-sheet*), then 'negative mass' would be something that pushes space-time outwards (

*like a leaf-blower*).

Or until you prove this wrong, it's right.

Yep, which makes it 'accepted fact'. There's no such thing as absolute fact (unless you're religious), so I'd just call it 'fact'. The theory that if you jump out a window, you will fall down, is a fact -- it could be disproved at any time, but it's pretty well accepted for the time being.

**Edited by Hodgman, 21 September 2012 - 08:57 AM.**