Discrete Mathematical Structures by Pearson

Functions 3-15

a

1

, a

2

, a

3

, …, a

n

… or by {a

n

: n ∈ N} or by (a

n

).

In some cases, the domain of the sequence is the set {0, 1, 2, …} of non-negative integers rather

than N. In such a case, the sequence is denoted by a

0

, a

1

, a

2

, …, a

n.

If the elements listed in the sequence stop after m steps, m ∈ N, then the sequence is called a

finite sequence and is denoted by a

1

, a

2

, …, a

m

.

A sequence that is not finite is called an infinite sequence.

Note 3.2 The elements in a sequence may be all different or some may be repeated.

Example 1 The sequence 1,

1

2

,

1

3

, … may be represented by a

n

=

1

n

, n ∈ N.

The sequence begins with n = 1.

Example 2 The sequence 1,