Finite and infinite Sequence

the length of sequence defined number of terms in sequence.

a sequence of finite length n called n-tuple. finite sequences include empty sequence ( ) has no elements.

normally, term infinite sequence refers sequence infinite in 1 direction, , finite in other—the sequence has first element, no final element. such sequence called singly infinite sequence or one-sided infinite sequence when disambiguation necessary. in contrast, sequence infinite in both directions—i.e. has neither first nor final element—is called bi-infinite sequence, two-way infinite sequence, or doubly infinite sequence. function set z of integers set, such instance sequence of integers ( …, −4, −2, 0, 2, 4, 6, 8… ), bi-infinite. sequence denoted



(
2
n

)

n
=
−
∞


∞




{\displaystyle (2n)_{n=-\infty }^{\infty }}

.