There are twelve dancing couples-three for each of
the four. How do you know? You count them.”
Multiplication is commonly said to be repeated
addition. This is false. Repeated addition helps you
count the crossings but the crossings and the
notion of ‘for each’ are the heart of the issue. If
multiplication were repeated addition, 4/
7 2/
5
would be repeated addition, a notion that is pretty
hard to defend.