Order of the Dannebrog

The Order of the Dannebrog (Danish: Dannebrogordenen) is an Order of Denmark, instituted in 1671 by Christian V. Until 1808, membership in the order was limited to fifty members of noble or royal rank who formed a single class known as White Knights to distinguish them from the Blue Knights who were members of the Order of the Elephant. In 1808, the Order was reformed and divided into four classes, with the ranks:

The Grand Cross can, as a special honor, be awarded "with diamonds". There is also a Cross of Honour (D.Ht.) (Dannebrogordens Hæderstegn).

The Grand Commander class is reserved to persons of princely origin. It is only awarded to Royals with close family ties with the Danish Royal House. The statute of the Order was amended in 1951 by a Royal Ordinance so that both men and women could be members of the Order.

Today, the Order of the Dannebrog is a means of honouring and rewarding the faithful servants of the modern Danish state for meritorious civil or military service, for a particular contribution to the arts, sciences or business life or for those working for Danish interests.

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.