

It Ain't No Repeated Addition - signa11
http://www.maa.org/devlin/devlin_06_08.html

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gizmo686
I'm somewhat of a hobbyist mathematician (and high school student). In my
experience, the problem the article is describing is one of the joys of math.
You start with the basic concept of repeated addition. Then you ask what
happens if I add this number to itself 5 + 1/2 times, and does that even make
sense. And sure enough it does make sense, if the number is 10, you add it to
itself 4 times, then you add it another half time, which is the same as adding
half of 10, or 5. This definition remains consistent with (or is) the original
conceptually, and, more excitingly, most of your favorite thearoms on
multiplication are still true. Then you discover irrational numbers, and
conceptually you can expand your definition of multiplication with ease.

