# What is sequence?

## Sequence

In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.

### Some articles on sequence:

Farey Sequence
... In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than ... Each Farey sequence starts with the value 0, denoted by the fraction 0⁄1, and ends with the value 1, denoted by the fraction 1⁄1 (although some authors omit these terms) ... A Farey sequence is sometimes called a Farey series, which is not strictly correct, because the terms are not summed ...
Translation (biology) - Genetic Code
... using sophisticated algorithms, the amino acid sequence, called primary structure, can be determined solely from the nucleic acid sequence with the aid of a translation table ... with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS) ... There are many computer programs capable of translating a DNA/RNA sequence into a protein sequence ...
Typical Set
... theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution ... of typicality is only concerned with the probability of a sequence and not the actual sequence itself ... provides a theoretical means for compressing data, allowing us to represent any sequence Xn using nH(X) bits on average, and, hence, justifying the use of entropy as a ...
Lebesgue's Monotone Convergence Theorem - Theorem
... Let be a pointwise non-decreasing sequence of -valued Σ–measurable functions, i.e ... k ≥ 1 and every x in X, Next, set the pointwise limit of the sequence to be f ... If the sequence satisfies the assumptions μ–almost everywhere, one can find a set N ∈ Σ with μ(N) = 0 such that the sequence is non-decreasing for every ...

### More definitions of "sequence":

• (verb): Arrange in a sequence.
• (noun): Film consisting of a succession of related shots that develop a given subject in a movie.
Synonyms: episode
• (noun): Several repetitions of a melodic phrase in different keys.
• (verb): Determine the order of constituents in.
Example: "They sequenced the human genome"
• (noun): Serial arrangement in which things follow in logical order or a recurrent pattern.
Example: "The sequence of names was alphabetical"; "he invented a technique to determine the sequence of base pairs in DNA"
• (noun): The action of following in order.
Example: "He played the trumps in sequence"
Synonyms: succession