## Quick Reference

Of two sets *S* and *T*. The set of all ordered pairs of the form (*s*,*t*) with the property that *s* is a member of *S* and *t* is a member of *T*; this is usually written as *S* × *T*. Formally,*S* × *T* = {(*s*,*t*)|(*s* ∈ *S*) and (*t* ∈ *T*)}If *R* denotes the set of real numbers, then *R* × *R* is just the set of points in the (Cartesian) plane or it can be regarded as the set of complex numbers, hence the name.

*S* × *T* = {(*s*,*t*)|(*s* ∈ *S*) and (*t* ∈ *T*)}

The concept can be extended to deal with the Cartesian product of *n* sets,*S*_{1},*S*_{2},…,*S** _{n}*This is the set of ordered

*n*-tuples(

*s*

_{1},

*s*

_{2},…,

*s*

*)with the property that each*

_{n}*s*

*is in*

_{i}*S*

*. In the case where each*

_{i}*S*

*is the same set*

_{i}*S*, it is customary to write

*S*

*for*

^{n}*S*×

*S*× …

*S*(

*n*terms)

*S*_{1},*S*_{2},…,*S*_{n}

(*s*_{1},*s*_{2},…,*s** _{n}*)

*S* × *S* × … *S* (*n* terms)

*Subjects:*
Computing.