An order or order of merit is a visible honour awarded by a sovereign state, monarch, dynastic house or organisation to a recipient, typically in recognition of individual merit.
The modern distinction between orders and decorations is somewhat vague, except that most historic chivalric orders imply a membership in a group, typically a confraternity. In a few exclusive European orders, membership is or was also limited in number. Decorations seldom have such limitations. Orders often come in multiple classes, including knights and dames, which may or may not be parallelled in decorations.
Modern orders of merit and decorations can trace their origin back to the monarchical and honorific orders of chivalry as established in the Middle Ages. While these were "societies, fellowships and colleges of knights", created by European monarchs in imitation of the military orders of the Crusades, granting membership in such societies gradually developed into an honour that could be bestowed in recognition of service or to ensure the loyalty of a certain clientele. Some of modern Europe's highest honours, such as the Order of the Golden Fleece, England's Order of the Garter, Denmark's Order of the Elephant and Scotland's Order of the Thistle, were created during that era. They were essentially courtly in nature, characterised by close personal relations between the orders' members and the orders' sovereign.
The Order of Merit (French: Ordre du Mérite) is a dynastic order recognising distinguished service in the armed forces, science, art, literature, or for the promotion of culture. Established in 1902 by King Edward VII, admission into the order remains the personal gift of its Sovereign—currently Edward VII's great-granddaughter, Queen Elizabeth II—and is restricted to a maximum of 24 living recipients from the Commonwealth realms plus a limited number of honorary members. While all members are awarded the right to use the post-nominal letters OM and a medallion for life, the Order of Merit's precedence among other honours differs between realms.
The first mention of a possible Order of Merit was made following the Battle of Trafalgar in 1805, in correspondence between First Lord of the Admiralty Lord Barham and William Pitt, though nothing came of the idea. Later, it was thought by Queen Victoria, her courtiers, and politicians alike, that a new order, based on the Prussian order Pour le Mérite, would make up for the insufficient recognition offered by the established honours system to achievement outside of public service, in fields such as art, music, literature, industry, and science.
The Lebanese Order of Merit was created by decision No. 1080 (dated 16 January 1922) and is regulated by the code of decorations decree (Law 122 dated 12 June 1959).
This order consists of two dignities and four ordinary classes as follows:
In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error committed" while replacing the asymptotic size, or asymptotic mean size, of an arithmetical function, by the value, or mean value, it takes at a large finite argument. A famous example is the problem of estimating the remainder term in the prime number theorem.
Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation.