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Originally Posted by Qfwfq
It isn't contra-reality, no. I'ts in contradiction with Peano's axioms. It's also false in the various Z_n groups. OTOH, 4 + 8 = 3 is false in N but true in Z_9.
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Okay. In abstract math perhaps.
I guess when I use "reality" I am talking physics. In those formulas which scientists use to describe physical reality, it is rare to find an integer. There are some squares and cubes, but those define something you DO to the term; you multiply it times itself.
I dare to say that nowhere in physical formulas do you find numbers (real or integer) where the base of that number is of any importance or consequence at all. The formulas that are composed of variables (or numeric constants such as pi*) do NOT assume or even need a particular numeric base.
We can generalize this to: ALL physical formula which define or describe the natural world are INDEPENDENT of numeric base; the truths they represent do not depend on using a particular base.
Even in college algebra, one learns that the properties of mathematical functions are independent of base. A=B ; B=C ; therefore A=C. This works in ALL bases. The same for AB = BA, in those algebras where multiplication [what's the word?!] conjugates {?}.
*pi can be expressed in any base, or as the abstract ratio of circumference to radius of a circle.
