Order
The order relation cannot be extended to in a meaningful way. Given a real number a, there is no convincing reason to decide that or that . Since can't be compared with any of the other elements, there's no point in using this relation at all. As another example, both and are true. However, order is used to make definitions in that are based on the properties of reals.
Read more about this topic: Real Projective Line
Famous quotes containing the word order:
“Therefore doth heaven divide
The state of man in divers functions,
Setting endeavor in continual motion,
To which is fixed, as an aim or butt,
Obedience; for so work the honeybees,
Creatures that by a rule in nature teach
The act of order to a peopled kingdom.”
—William Shakespeare (1564–1616)
“For it is owing to their wonder that men both now begin and at first began to philosophize.... And a man who is puzzled and wonders thinks himself ignorant ...; therefore since they philosophized in order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end.”
—Aristotle (384–322 B.C.)
“It is well within the order of things
That man should listen when his mate sings;
But the true male never yet walked
Who liked to listen when his mate talked.”
—Anna Wickham (1884–1947)