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This is a side track, and it isn't true in general. How do you add pi copies of √2?To me, there is no point in asking "why multiplication and not addition" since multiplication IS addition... 4*5 = 5+5+5+5 or 4+4+4+4+4, the result is the same.

See http://www.maa.org/devlin/devlin_06_08.html [Broken] and the follow-up article http://www.maa.org/devlin/devlin_0708_08.html [Broken].

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