An alphabet is a set of symbols. Some alphabets are infinite, such as the set of real numbers or the set of complex numbers. Usually, we will be interested in finite alphabets. A sequence is a string of symbols from a given alphabet. A sequence may be of infinite length. An infinite sequence may be periodic or aperiodic; infinite aperiodic sequences may become periodic after some initial segment. Any infinite sequence that we will consider has a fixed beginning, but is unending. It is possible, however, that an infinite sequence has neither a beginning nor an end.

A finite sequence is a string of symbols of finite length from the given alphabet. The blocklength of the sequence, denoted n, is the number of symbols in the sequence. Sometimes the blocklength is not explicitly specified, but is known implicitly only by counting the number of symbols in the sequence after that specific sequence is given. In other situations, the blocklength n is explicitly specified, and only sequences of blocklength n are under consideration.

There are a great many aspects to the study of sequences. One may study the structure and repetition of various subpatterns within a given sequence of symbols. Such studies do not need to presuppose any algebraic or arithmetic structure on the alphabet of the sequence.