English
order
Pronunciation
• (RP) IPA: /ˈɔːdə/
• (America) IPA: /ˈɔɹdɚ/, [ˈɔɹɾɚ]
Noun

order

1. (countable) Arrangement, disposition, or sequence.
2. (countable) A position in an arrangement, disposition, or sequence.
• 1897, Thomas Little Heath (translator), Eutocius of Ascalon, Extract from a commentary by Eutocius, quoted in 1897 [CUP], T. L. Heath (editor), The Works of Archimedes, 2002, Dover, unnumbered page ↗,
His attempt I shall also give in its order.
3. (uncountable) The state of being well arranged.
The house is in order; the machinery is out of order.
4. (countable) Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet.
to preserve order in a community or an assembly
5. (countable) A command.
6. (countable) A request for some product or service; a commission to purchase, sell, or supply goods.
7. (countable) 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.
8. (countable) An association of knights.
the Order of the Garter, the Order of the Bath.
9. Any group of people with common interests.
10. (countable) 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.
11. (countable, taxonomy) A rank in the classification of organisms, below class and above family; a taxon at that rank.
Magnolias belong to the order Magnoliales.
12. 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
They are in equal order to their several ends.
Various orders various ensigns bear.
[…] which, to his order of mind, must have seemed little short of crime.
13. (chiefly plural) An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry.
to take orders, or to take holy orders, that is, to enter some grade of the ministry
14. (architecture) The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (since the column and entablature are the characteristic features of classical architecture) a style or manner of architectural design.
15. (cricket) The sequence in which a side’s batsmen bat; the batting order.
16. (electronics) 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
17. (chemistry) The overall power of the rate law of a chemical reaction, expressed as a polynomial function of concentrations of reactants and products.
18. (set theory) The cardinality, or number of elements in a set, group, or other structure regardable as a set.
• 1911 [Cambridge University Press], William Burnside, Theory of Groups of Finite Order, 2nd Edition, Reprint, Dover (Dover Phoenix), 2004, page 222 ↗,
In this case, the conjugate set contains n(n − 1)/x(x − 1) distinct sub-groups of order m, and H is therefore self-conjugate in a group K of order x(x − l)m.
• 2000, Michael Aschbacher, Finite Group Theory, Cambridge University Press, 2nd Edition, page 260 ↗,
For various reasons it turns out to be better to enlarge this set of invariants to include suitable normalizers of subgroups of odd prime order.
19. (group theory, of an element of a group) For given group G and element gG, 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).
• 1997, Frank Celler, C. R. Leedham-Green, Calculating the Order of an Invertible Matrix, Larry Finkelstein, William M. Kantor (editors), Groups and Computation II, American Mathematical Society, page 55 ↗,
The object of this note is to observe that it is possible to calculate the order of an element A of G = \mathit{GL}(d,q) on average using O(d^3 \mathsf{log}\ q) field operations, assuming that q^i-1 has been factorised for i\le d.
• 1999, A. Ehrenfeucht, T. Harju, G. Rozenberg, The Theory of 2-structures, World Scientific, page 15 ↗,
If \Delta is a finite group, its cardinality is called the order of \Delta. The order of an element a \in \Delta is defined as the smallest nonnegative integer n such that a^n = 1_\Delta. The second case of the following result is known as Cauchy's theorem.
Theorem 1.10 Let \Delta be a finite group.
(i) The order of an element a \in \Delta divides the order |\Delta| of the group.
(ii) If a prime number p divides |\Delta|, then there exists an element a \in \Delta of order p.
• 2010, A. R. Vasishta, A. K. Vasishta, Modern Algebra, Krishna Prakashan Media, 60th Edition, page 180 ↗,
Since in a finite group the order of an element must be a divisor of the order of the group, therefore o (a) cannot be 3 and so we must have o (a)=4=the order of the group G.
20. (graph theory) The number of vertices in a graph.
21. (order theory) A partially ordered set.
22. (order theory) The relation on a partially ordered set that determines that it is, in fact, a partially ordered set.
23. (algebra) 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.
24. (finance) A written direction to furnish someone with money or property; compare money order, postal order.
• 1763, James Boswell, in Gordon Turnbull (ed.), London Journal 1762–1763, Penguin 2014, p. 233:
I then walked to Cochrane's & got an order on Sir Charles Asgill for my money.
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• French: ordre
• Russian: поря́док
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• French: relation d'ordre
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Verb

order (orders, present participle ordering; past and past participle ordered)

1. (transitive) To set in some sort of order.
2. (transitive) To arrange, set in proper order.
3. (transitive) To issue a command to.