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:
“He had killed and put to earth so many that his sword broke in two. At length he thought to himself that that was enough massacring and killing for one day, and that the rest should be allowed to escape in order to spread the news.”
—François Rabelais (1494–1553)
“Woman ... cannot be content with health and agility: she must make exorbitant efforts to appear something that never could exist without a diligent perversion of nature. Is it too much to ask that women be spared the daily struggle for superhuman beauty in order to offer it to the caresses of a subhumanly ugly mate?”
—Germaine Greer (b. 1939)
“Kicking his mother until she let go of his soul
Has given his a healthy appetite: clearly, her role
In the New Order must be
To supply and deliver his raw materials free;”
—W.H. (Wystan Hugh)