I am learning about the cartesian product as defined by The New Oxford American Dictionary as:
the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ( x, y) for which x belongs to X and y belongs to Y.
How can I use this in life? A simple practical example would help a lot.
A certain kind of Lacoste pullovers comes in five colors, three different neck forms, and in six sizes. Let $$\eqalign{C&:=\{{\rm blue,\ red,\ yellow,\ green,\ brown}\}\ ,\cr N&:=\{{\rm round\ neck, \ V{-} neck,\ polo{-}neck}\}\ ,\cr S&:=\{{\rm XS,\ S,\>M,\ L,\ XL,\ XXL}\}\cr}$$ be the sets of colors, neck forms, and sizes, respectively. Then the set of all variants to be manufactured is the triple cartesian product $C\times N\times S$, and consists of $5\cdot 3\cdot 6=90$ elements. As a store manager selling this kind of sweater you would have to make room for $90$ heaps.