Cartesian Product of a Set with Itself

When a set is multiplied by itself, $A\times A = A^2 = \{(a,b)/a,b\in A\}$, where $(a,b)$ is an ordered pair. Extending further, $A^3 = A\times A\times A = \{(a,b,c)/a,b,c\in A\}$, where $(a,b,c)$ is an ORDERED TRIPLET. For example, if $A=\{4,5\}$, then $A^2 = A\times A = \{(4,4),(4,5),(5,4),(5,5)\}$ (4 pairs), and $A^3 = A\times A\times A = \{(4,4,4),(4,4,5),(4,5,4),(4,5,5),(5,4,4),(5,4,5),(5,5,4),(5,5,5)\}$ (8 triplets). …