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Re: 2 simple? questions and proposed answers
Posted:
Jan 29, 2012 7:50 AM


Please, see a good and extensive discussion on the (a)(b) = ab issue in Mazur?s delightful book Imagining Numbers (a tothepoint summary of the discussion is given on page 102). Also, Honsberger?s Mathematical Delights gives a discussion on a nice geometric representation of multiplication where (a)(b) = ab pops up as a special case. (See Section 5, pp. 53.)
Finally, let me tell you a story which migth convince nonmathematical people that (1)(5) = 5: I have some friends which each has lent me 5 dollars, so for me this is totally Nx(5) dollars. It is fair to say that if I had no friends (bad for me), then this would be 0x(5) = 0 dollars. If I pay back one of my friends, for me this means (N1)x(5) dollars, which must be Nx(5) + 5 dollars. If this is also true in the case N = 0, we have (01)x(5) = 0x(5) + 5. Now, the LHS here is equal to (1)(5) and the RHS is equal to 0 + 5 = 5; so LHS = RHS gives (1)(5) = 5. Convinced? (Of course, the distributive law is lurking behind the scene.)



