This argument applies no matter what finite set we began with.
In fact, any finite set of generators provides an example.
A language is a finite or infinite set of strings.
When each state has only a finite set of children, this won't happen.
Let E be a finite set and k a natural number.
A process can be divided into a finite set of processes with similar properties.
Let be a finite set of events determined by these variables.
On the other hand, a finite set might be connected.
C is a finite set called the clocks of A.
Let be a finite set, representing a collection of people.