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.
The Military Order of the Tower and of the Sword, of Valour, Loyalty and Merit (Portuguese: Ordem Militar da Torre e Espada do Valor, Lealdade e Mérito) is a Portuguese order of knighthood and the pinnacle of the Portuguese honours system. It was created by King Afonso V in 1459. The order may be bestowed on people or on Portuguese municipalities.
The order was originally created by King Afonso V of Portugal in 1459, under the name of the Order of the Sword, inspired by the legend that Arab rule in Africa would end when a Christian prince would besiege the fortress at Fez. Knighthood in the Order of the Sword was given as reward to those who participated in the conquests and battles in Africa. The order fell into disuse after the conquest of Tangiers and Asilah.
The order was revived on 29 November 1808, by Prince Regent John, later John VI of Portugal. It commemorated the safe arrival of the Royal Family in the Portuguese colony of Brazil, after Napoleon had invaded Portugal. Its full title was “the Royal Order of the Tower and Sword”. It was available to both Portuguese and foreigners and for military, political or civilian achievement. Among the intended recipients were subjects of His Britannic Majesty, who had assisted the Royal Family to reach Brazil, but who were ineligible for the other Portuguese orders due to their religion.
A choice to make
A narrow road and no easy answers
Make a stand today
Small is the gate and hardship's what you'll face
Do you see what i've become
Or would you stop what i've begun
If your scorn is my gain then get out of my way
And i'll see you on the road
If i have the strength for this
Will i be the one to stand alone?
And if i can overcome
Will i be the better man for it?
This is the sword that divides us all
Make one wrong move and watch me fall
The burden of the choices made
How high the price
Never thought you'd pay
These wounds run deep, see
The fears as they creep
Now left alone
Abandoned and cold
Deserted, defeated
For the things that you believe in
If they turned their back to you
If they all just turned away from you
All from those who you thought you knew