Infinite sequence

Finite and infinite

Normally, the term infinite sequence refers to a sequence that is infinite in one direction, and finite in the other; such a sequence has a first element, but no final element, and are called singly infinite sequence or a one-sided infinite sequence when other is needed. In contrast, a sequence that is infinite in both directions—i.e. that has neither a first nor a final element—is called a bi-infinite sequence, two-way infinite sequence, or doubly infinite sequence. A function from ${\displaystyle \mathbb {Z} }$ the set of allintegers, into a set, for example the sequence of all even integers (..., −4, −2, 0, 2, 4, 6, 8, ...), is bi-infinite. This sequence could be denoted ${\textstyle {(2n)}_{n=-\infty }^{\infty }}$.