The cartesian power of a set X can be defined as:

The formal definition of an iterated function on a set X follows.

Figure 1 represents the set X painted grey and some boxes.

The set X is the set of all positions in your house.

The set X is the set of all such sequences.

Some important types of binary relations over a set X are:

The effective packing dimension of a set X is .

Note that each member of the set X is a point in .

The set X can be termed the closed upper half plane.

The set X and the empty set are open sets.