Definition of "order"

In these situations we find the Genesee slate, the Tully limestone and the upper part of the Hamilton group, each one in its order disappearing beneath the lake level as we proceed southward.

1843, New York (State). Natural History Survey, Geology of New-York: Comprising the survey of the fourth geological ...‎

In the latter portion of this period, the country was assailed by famine and pestilence - — a fearful visitation which will be noticed hereafter in its order of date, and of which it would be out of place to say more at present.

1856, George Nicholls, A History of the Irish Poor Law: In Connexion with the Condition of the People‎

His attempt I shall also give in its order.

1897, T. L. 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

This narrative must be discussed later on, in its order.

1915, Edwin Abbott Abbott, the fourfold gospel the proclamation of the new kingdom‎, page 298

The latter comes into play only as we examine each word in its order in the line.

1996, John Clare, Eric Robinson, David Powell, John Clare: Poems of the Middle Period, 1822-1837‎, page xxxi

Hasn't it been shown that the Hebrew letter “w” is equivalent to the number 6, due to its order in the alphabet, he asked?

2013, Leah Sarat, Fire in the Canyon: Religion, Migration, and the Mexican Dream‎

Because Professor Soler told me that you had to investigate things step by step, that you had to find a thread to follow and follow it, and find everything out in its order.

2014, Julia Navarro, Tell Me Who I Am‎

It was by his order the shattered leading company flung itself into the houses when the Sin Verguenza were met by an enfilading volley as they reeled into the calle.

1907, Harold Bindloss, chapter 30, in The Dust of Conflict‎

John Hedley was Locomotive Foreman at Beattock. He was in bed, but they roused him, and he gave orders for one of his pilot engines to go up to the summit, get Mitchell's train, and take it to Carlisle.

1950 January, David L. Smith, “A Runaway at Beattock”, in Railway Magazine, page 53

A farmer could place an order for a new tractor part by text message and pay for it by mobile money-transfer.

2012 December 1, “An internet of airborne things”, in The Economist‎, volume 405, number 8813, page 3 (Technology Quarterly)

The Order of Propitious Clouds is a civilian order that can be awarded to Taiwan citizens or foreign nationals. It is divided into a total of nine "classes" or grades, of which the Special Grand Cordon is the highest.Pelosi said she was particularly honored to receive the award from Tsai -- "a woman president in one of the freest societies in the world."

2022 August 3, Matthew Mazzetta, “President Tsai awards state honor to visiting U.S. House speaker”, in Focus Taiwan‎, archived from the original on 03 August 2022

Bats host many high-profile viruses that can infect humans, including severe acute respiratory syndrome and Ebola. A recent study explored the ecological variables that may contribute to bats’ propensity to harbor such zoonotic diseases by comparing them with another order of common reservoir hosts: rodents.

2013 May-June, Katie L. Burke, “In the News”, in American Scientist, volume 101, number 3, page 193

They are in equal order to their several ends.

1651, Jer[emy] Taylor, The Rule and Exercises of Holy Living. […], 2nd edition, London: […] Francis Ashe […]

Various orders various ensigns bear.

1726, George Granville, The British Enchanters

[…] which, to his order of mind, must have seemed little short of crime.

1850, Nathaniel Hawthorne, The Scarlet Letter, a Romance, Boston, Mass.: Ticknor, Reed, and Fields

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.

1911 [Cambridge University Press], William Burnside, Theory of Groups of Finite Order, 2nd Edition, Reprint, Dover (Dover Phoenix), 2004, page 222

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.

2000, Michael Aschbacher, Finite Group Theory, 2nd edition, Cambridge University Press, page 260

The object of this note is to observe that it is possible to calculate the order of an element A {\displaystyle A} of G = G L ( d , q ) {\displaystyle G={\mathit {GL}}(d,q)} on average using O ( d 3 l o g q ) {\displaystyle O(d^{3}{\mathsf {log}}\ q)} field operations, assuming that q i − 1 {\displaystyle q^{i}-1} has been factorised for i ≤ d {\displaystyle i\leq d} .

1997, Frank Celler, C. R. Leedham-Green, “Calculating the Order of an Invertible Matrix”, in Larry Finkelstein, William M. Kantor, editors, Groups and Computation II, American Mathematical Society, page 55

If Δ {\displaystyle \Delta } is a finite group, its cardinality is called the order of Δ {\displaystyle \Delta } . The order of an element a ∈ Δ {\displaystyle a\in \Delta } is defined as the smallest nonnegative integer n {\displaystyle n} such that a n = 1 Δ {\displaystyle a^{n}=1_{\Delta }} . The second case of the following result is known as Cauchy's theorem. / Theorem 1.10 Let Δ {\displaystyle \Delta } be a finite group. (i) The order of an element a ∈ Δ {\displaystyle a\in \Delta } divides the order | Δ | {\displaystyle |\Delta |} of the group. (ii) If a prime number p {\displaystyle p} divides | Δ | {\displaystyle |\Delta |} , then there exists an element a ∈ Δ {\displaystyle a\in \Delta } of order p {\displaystyle p} .

1999, A. Ehrenfeucht, T. Harju, G. Rozenberg, The Theory of 2-structures, World Scientific, page 15

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.

2010, A. R. Vasishta, A. K. Vasishta, Modern Algebra, Krishna Prakashan Media, 60th Edition, page 180

I then walked to Cochrane's & got an order on Sir Charles Asgill for my money.

1763, James Boswell, edited by Gordon Turnbull, London Journal 1762-1763, Penguin, published 2014, page 233

persons presented to be ordered deacons

1549 March 7, Thomas Cranmer [et al.], compilers, The Booke of the Common Prayer and Administration of the Sacramentes, […], London: […] Edowardi Whitchurche […]