Chivalric order

A chivalric order, order of chivalry or equestrian order is an order, confraternity or society of knights typically founded during or in inspiration of the original Catholic military orders of the Crusades (circa 1099-1291), paired with medieval concepts of ideals of chivalry.

Modern historiography tends to take the fall of Acre in 1291 as the end of the age of the crusades. In contemporary understanding, many further crusades against the Ottoman Empire were planned and partly executed throughout the 14th century and well into the 15th century. The late medieval chivalric orders understood themselves as reflecting an ongoing military effort against Islam, even though such an effort, with the rise of the Ottoman Empire and the Fall of Constantinople in the 1450s, was without realistic hope of success.

During the 15th century, orders of chivalry, or orders of knighthood, became a mere courtly fashion that could be created ad hoc, some of them purely honorific, consisting of nothing but the badge. These institutions in turn gave rise to the modern-day orders of merit.

Big O notation

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.