Product set/Chess board/Example

A chess board (meaning the set of squares of a chess board where a chess piece may stand) is the product set ${}\{a,b,c,d,e,f,g,h\}\times \{1,2,3,4,5,6,7,8\}$. Every square is a pair, e.g. ${}(a,1),(d,4),(c,7)$. Because the two component sets are different, one may write instead of pair notation simply ${}a1,d4,c7$. This notation is the starting point to describe chess positions, and complete chess games.