Infinite Sequence

An infinite sequence is a real function whose domain is the set of all positive integers.

A sequence a can be displayed in the form

a(1),a(2),...,a(H),....

The value a(n) is called the nth term of the sequence and is usually written a_n. The whole sequence is denoted by

<a_n> = a₁, a₂,... , a_n,....

Hyperintegers, which were introduced in Section 3.8, are a basic tool in this chapter. Since an is defined for every positive integer n, a_H is defined for every positive infinite hyperinteger H.