Ranked

A ranking is a relationship between a set of items such that, for any two items, the first is either 'ranked higher than', 'ranked lower than' or 'ranked equal to' the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered.

Famous quotes containing the word ranked:

“If to be venerated for benevolence, if to be admired for talents, if to be esteemed for patriotism, if to be beloved for philanthropy, can gratify the human mind, you must have the pleasing consolation to know that you have not lived in vain. And I flatter myself that it will not be ranked among the least grateful occurrences of your life to be assured that, so long as I retain my memory, you will be thought on with respect, veneration, and affection by your sincere friend.”
—George Washington (1732–1799)

“There exists a kind of laughter which is worthy to be ranked with the higher lyric emotions and is infinitely different from the twitchings of a mean merrymaker.”
—Nikolai Vasilyevich Gogol (1809–1852)

“The trumpets sound, the banners fly,
The glittering spears are ranked ready;
The shouts o’ war are heard afar,
The battle closes thick and bloody;
But it’s no the roar o’ sea or shore
Wad mak me langer wish to tarry;
Nor shout o’ war that’s heard afar,
Its leaving thee, my bonnie Mary.”
—Robert Burns (1759–1796)