Quote:
Originally Posted by Ralph Sir Edward
What is 2 + 2 equal? 4? I say 10, but I can live with 11. Why not? They're all correct. It all has to do with your underlying postulates. 2 + 2 = 11 is correct - for number in base 3. 2 + 2 = 10 is correct in base 4. 2 + 2 = 4 is correct for base 5 and above.
This isn't cheating. All mathematics have to a starting set of assumptions, called postulates (or axioms). Which set is right? Why, all of them! Each one leads to a different mathematics. Euclidean Geometry was based on a particular set of assumptions, change one of the assumptions and, voila, a new non-Euclidean geometry. The only way to say whether a mathematic is "valid" is if it's calculations match up with some measurements in the "real world". If they don't, they may not be "valid" but they're still perfectly rational, and may match up with something somewhere in the Multiverse (or Macrocosmic All, if your prefer).
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You are confusing axioms with symbols systems and number system. In whatever number system you choose, that number represented by "2" in an Arabic number system to base ten, added to "2" in that system is equal to that number represented by "4" in that system. How you represent this is irrelevant.