# Sequence vs. Order

By Jaxson

• Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order matters. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first n natural numbers (for a sequence of finite length n). The position of an element in a sequence is its rank or index; it is the integer from which the element is the image. It depends on the context or a specific convention, if the first element has index 0 or 1. When a symbol has been chosen for denoting a sequence, the nth element of the sequence is denoted by this symbol with n as subscript; for example, the nth element of the Fibonacci sequence is generally denoted Fn.

For example, (M, A, R, Y) is a sequence of letters with the letter ‘M’ first and ‘Y’ last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, …). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory; infinite sequences are called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

Wikipedia
• Sequence (noun)

A set of things next to each other in a set order; a series

• Sequence (noun)

A series of musical phrases where a theme or melody is repeated, with some change each time, such as in pitch or length (example: opening of Beethoven’s Fifth Symphony).

• Sequence (noun)

A musical composition used in some Catholic Masses between the readings. The most famous sequence is the Dies Irae (Day of Wrath) formerly used in funeral services.

• Sequence (noun)

An ordered list of objects, typically indexed with natural numbers.

• Sequence (noun)

A subsequent event; a consequence or result.

• Sequence (noun)

A series of shots that depict a single action or style in a film, television show etc.

• Sequence (noun)

A meld consisting of three or more cards of successive ranks in the same suit, such as the four, five and six of hearts.

• Sequence (verb)

to arrange in an order

• Sequence (verb)

to determine the order of things, especially of amino acids in a protein, or of bases in a nucleic acid

• Sequence (verb)

to produce (music) with a sequencer

• Order (noun)

Arrangement, disposition, or sequence.

• Order (noun)

A position in an arrangement, disposition, or sequence.

• Order (noun)

The state of being well arranged.

“The house is in order; the machinery is out of order.”

• Order (noun)

Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet.

“to preserve order in a community or an assembly”

• Order (noun)

A command.

• Order (noun)

A request for some product or service; a commission to purchase, sell, or supply goods.

• Order (noun)

A group of religious adherents, especially monks or nuns, set apart within their religion by adherence to a particular rule or set of principles

“St. Ignatius Loyola founded the Jesuit order in 1537.”

• Order (noun)

An association of knights

“the Order of the Garter, the Order of the Bath.”

• Order (noun)

any group of people with common interests.

• Order (noun)

A decoration, awarded by a government, a dynastic house, or a religious body to an individual, usually for distinguished service to a nation or to humanity.

• Order (noun)

A rank in the classification of organisms, below class and above family; a taxon at that rank.

“Magnolias belong to the order Magnoliales.”

• Order (noun)

A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a distinct character, kind, or sort.

“the higher or lower orders of society”

“talent of a high order”

• Order (noun)

An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; often used in the plural.

“to take orders, or to take holy orders, that is, to enter some grade of the ministry”

• Order (noun)

The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (as the column and entablature are the characteristic features of classical architecture) a style or manner of architectural designing.

• Order (noun)

The sequence in which a side’s batsmen bat; the batting order.

• Order (noun)

a power of polynomial function in an electronic circuit’s block, such as a filter, an amplifier, etc.

“a 3-stage cascade of a 2nd-order bandpass Butterworth filter.”

• Order (noun)

The overall power of the rate law of a chemical reaction, expressed as a polynomial function of concentrations of reactants and products.

• Order (noun)

The cardinality, or number of elements in a set, group, or other structure regardable as a set.

• Order (noun)

For given group G and element g ∈ G, the smallest positive natural number n, if it exists, such that (using multiplicative notation), gn = e, where e is the identity element of G; if no such number exists, the element is said to be of infinite order (or sometimes zero order).

• Order (noun)

The number of vertices in a graph.

• Order (noun)

A partially ordered set.

• Order (noun)

The relation on a partially ordered set that determines that it is, in fact, a partially ordered set.

• Order (noun)

The sum of the exponents on the variables in a monomial, or the highest such among all monomials in a polynomial.

“A quadratic polynomial, a x^2 + b x +c, is said to be of order (or degree) 2.”

• Order (verb)

To set in some sort of order.

• Order (verb)

To arrange, set in proper order.

• Order (verb)

To issue a command to.

“He ordered me to leave.”

• Order (verb)

To request some product or service; to secure by placing an order.

“to order groceries”

• Order (verb)

To admit to holy orders; to ordain; to receive into the ranks of the ministry.

Wiktionary
• Sequence (noun)

a particular order in which related things follow each other

“the poems should be read in sequence”

“the content of the programme should follow a logical sequence”

• Sequence (noun)

a repetition of a phrase or melody at a higher or lower pitch

“a restless search for interesting harmonic sequences”

• Sequence (noun)

the order in which amino-acid or nucleotide residues are arranged in a protein, DNA, etc.

“these are enzymes which will cleave only at specific base sequences in the DNA”

• Sequence (noun)

a set of related events, movements, or items that follow each other in a particular order

“a gruelling sequence of exercises”

“a sonnet sequence”

• Sequence (noun)

a set of three or more playing cards of the same suit next to each other in value, for example 10, 9, 8.

• Sequence (noun)

an infinite ordered series of numerical quantities.

• Sequence (noun)

a part of a film dealing with one particular event or topic

“the famous underwater sequence”

• Sequence (noun)

(in the Eucharist) a hymn said or sung after the Gradual or Alleluia that precedes the Gospel.

• Sequence (verb)

arrange in a particular order

“trainee librarians decide how a set of misfiled cards could be sequenced”

• Sequence (verb)

ascertain the sequence of amino-acid or nucleotide residues in (a protein, DNA, etc.)

“independent clones were analysed by DNA sequencing”

“we have undertaken to isolate and sequence the rat retinoblastoma cDNA”

• Sequence (verb)

play or record (music) with a sequencer.

• Order (noun)

the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method

“I filed the cards in alphabetical order”

• Order (noun)

a state in which everything is in its correct or appropriate place

“she tried to put her shattered thoughts into some semblance of order”

• Order (noun)

a state in which the laws and rules regulating public behaviour are observed and authority is obeyed

“the army was deployed to keep order”

• Order (noun)

the prescribed or established procedure followed by a meeting, legislative assembly, debate, or court of law

“the meeting was called to order”

• Order (noun)

a stated form of liturgical service, or of administration of a rite, prescribed by ecclesiastical authority.

• Order (noun)

an authoritative command or instruction

“he was not going to take orders from a mere administrator”

“the skipper gave the order to abandon ship”

• Order (noun)

a verbal or written request for something to be made, supplied, or served

“the firm has won an order for six tankers”

• Order (noun)

a thing made, supplied, or served as a result of an order

“he would deliver special orders for the Sunday dinner”

• Order (noun)

a written direction of a court or judge

“she was admitted to hospital under a guardianship order”

• Order (noun)

a written direction to pay money or deliver property.

• Order (noun)

a particular social, political, or economic system

“they were dedicated to overthrowing the established order”

• Order (noun)

a social class

“the upper social orders”

• Order (noun)

a rank in the Christian ministry, especially that of bishop, priest, or deacon.

• Order (noun)

the rank of a member of the clergy or an ordained minister of the Church

“he took priest’s orders”

• Order (noun)

any of the nine grades of angelic beings in the celestial hierarchy as formulated by Pseudo-Dionysius.

• Order (noun)

a society of monks, nuns, or friars living under the same religious, moral, and social regulations and discipline

“the Franciscan Order”

• Order (noun)

a society of knights bound by a common rule of life and having a combined military and monastic character

“the Templars were also known as the Order of Christ”

• Order (noun)

an institution founded by a monarch along the lines of a medieval crusading monastic order for the purpose of honouring meritorious conduct.

• Order (noun)

the insignia worn by members of an order of honour or merit.

• Order (noun)

a Masonic or similar fraternity.

• Order (noun)

the quality or nature of something

“poetry of the highest order”

• Order (noun)

the overall state or condition of something

“the house had only just been vacated and was in good order”

• Order (noun)

a principal taxonomic category that ranks below class and above family

“the higher orders of insects”

• Order (noun)

any of the five classical styles of architecture (Doric, Ionic, Corinthian, Tuscan, and Composite) based on the proportions of columns and the style of their decoration.

• Order (noun)

any style of architecture subject to uniform established proportions.

• Order (noun)

equipment or uniform for a specified purpose or of a specified type

“the platoon changed from drill order into PT kit”

• Order (noun)

the position in which a rifle is held after ordering arms.

• Order (noun)

the degree of complexity of an equation, expression, etc., as denoted by an ordinal number.

• Order (noun)

the number of differentiations required to reach the highest derivative in a differential equation.

• Order (noun)

the number of elements in a finite group.

• Order (noun)

the number of rows or columns in a square matrix.

• Order (verb)

give an authoritative instruction to do something

“the judge ordered a retrial”

“she ordered me to leave”

“‘Stop frowning,’ he ordered”

“he ordered that the ship be abandoned”

• Order (verb)

continually tell someone to do things in an overbearing way

• Order (verb)

command (something) to be done or (someone) to be treated in a particular way

“he ordered the anchor dropped”

• Order (verb)

request (something) to be made, supplied, or served

“my mate ordered the tickets last week”

“I asked the security guard to order me a taxi”

“are you ready to order, sir?”

• Order (verb)

arrange (something) in a methodical way

“her normally well-ordered life”

“all entries are ordered by date”

Oxford Dictionary