Editing Double counting (proof technique) (section)

===Multiplication (of natural numbers) commutes===
This is a simple example of double counting, often used when teaching multiplication to young children. In this context, multiplication of [[natural number]]s is introduced as repeated addition, and is then shown to be [[Commutative_property|commutative]] by counting,  in two different ways, a number of items arranged in a rectangular grid.  Suppose the grid has <math>n</math> rows and <math>m</math> columns.  We first count the items by summing <math>n</math> rows of <math>m</math> items each, then a second time by summing <math>m</math> columns of <math>n</math> items each, thus showing that, for these particular values of <math>n</math> and <math>m</math>, <math>n \times m = m \times n</math>.