But, many of these index sets are even more complicated than the halting problem.

The index has two parts, the sequence set and index set.

The above definitions have been generalized to gradings ring using any monoid G as an index set.

If then is the index set of .

In these cases the index set may be implied by a listing of the first few abstract elements.

The set of values that the index can take on is called the index set.

Let be an index set and for all .

Stochastic processes can be classified according to the cardinality of its index set (usually interpreted as time) and state space.

When an enumeration is used in an ordered list context, we impose some sort of ordering structure requirement on the index set.

A family is indexed by an index set.