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Jul 18, 2011 at 22:19 comment added David Z @AndyS: excellent point. In fact, in some way it's kind of the same thing that happens when we use the speed of light to convert time into distance, or energy into momentum, etc. so that we can apply a Lorentz transformation to a 4-vector.
Jul 18, 2011 at 9:42 comment added yatima2975 @Saeed, if you do that, then presumably also 4 oranges + 3 apples = 7 fruits, from which you can derive 1 orange = 1 apple. You might as well call them fruits straight away!
Jul 17, 2011 at 4:39 comment added AndyS Then what you're really doing is defining a more general category, which contains both of the things you're adding. You're not really adding 5 apples and 2 oranges, you're just adding 5 fruits and 2 fruits. That's the only way for the units to factor out so that you can add the numbers. In multiplication it doesn't matter, for you can commute the numbers through the units, and so the product is well-defined.
Jul 17, 2011 at 4:25 comment added Saeed Neamati What if we make a new unit for addition? What if we say 5 oranges + 2 apples = 7 fruits or something like that?
Jul 17, 2011 at 0:50 history edited AndyS CC BY-SA 3.0
added 7 characters in body
Jul 16, 2011 at 22:42 history answered AndyS CC BY-SA 3.0