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:
“The confusion of emotions with behavior causes no end of unnecessary trouble to both adults and children. Behavior can be commanded; emotions can’t. An adult can put controls on a child’s behavior—at least part of the time—but how do you put controls on what a child feels? An adult can impose controls on his own behavior—if he’s grown up—but how does he order what he feels?”
—Leontine Young (20th century)
“Out of the slimy mud of words, out of the sleet and hail of verbal imprecisions,
Approximate thoughts and feelings, words that have taken the place of thoughts and feelings,
There springs the perfect order of speech, and the beauty of incantation.”
—T.S. (Thomas Stearns)
“There is no explanation for evil. It must be looked upon as a necessary part of the order of the universe. To ignore it is childish, to bewail it senseless.”
—W. Somerset Maugham (1874–1965)