Order of Pope Pius IX

The Order of Pope Pius IX (Italian: Ordine di Pio IX), also referred as the Pian Order (Italian: Ordine Piano), is a papal order of knighthood founded on 17 June 1847 by Pope Pius IX. Since November 1993, it has been granted to women.

Originally founded by Pope Pius IV in 1560, the awarding of the order fell into disuse and was re-instituted by Pope Pius IX as a continuation in 1847.

The highest rank awarded by the Pope is the gold Collar of the Order, awarded to heads of state on the occasion of official visits to the Holy See. The Grand Cross is the highest Papal award given to lay men and women, often given to Ambassadors accredited to the Holy See after two years in post as well as exceptional Catholics in the wider world for particular services, mainly in the international field and for outstanding deeds for Church and society.

The next rank is that of Knight (and now Dame) Commander, to whom the Star (the same as worn by the Grand Crosses) may be given as a higher distinction. The lowest rank is that of Knight or Dame. It is awarded to Catholics and non-Catholics and, on occasion, to non-Christians.

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.

Pope Pius IX

Pope Pius IX (Italian: Pio IX; 13 May 1792 – 7 February 1878), born Giovanni Maria Mastai-Ferretti, reigned as Pope from 16 June 1846 to his death in 1878. He was the longest-reigning elected pope in the history of the Catholic Church – over 31 years (the longest serving, un-elected pope was Peter the Apostle, posthumously considered the first pope, who was confirmed by Christ in 33 AD and killed by Emperor Nero in 67 AD). During his pontificate, he convened the First Vatican Council (1869–70), which decreed papal infallibility, but the council was cut short due to the loss of the Papal States.

Pius IX defined the dogma of the Immaculate Conception of the Blessed Virgin Mary, meaning that Mary was conceived without original sin. Pius IX also conferred the title Our Mother of Perpetual Help on a famous Byzantine icon from Crete entrusted to the Redemptorists.

He was also the last pope to rule as the Sovereign of the Papal States, which fell completely to the Italian army in 1870 and were incorporated into the Kingdom of Italy. After this, he was referred to – chiefly by himself – as the "Prisoner of the Vatican".