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:
“All things being equal, I would choose a woman over a man in order to even the balance of power, to insinuate a different perspective into the process, to give young women something to shoot for and someone to look up to. But all things are rarely equal.”
—Anna Quindlen (b. 1952)
“The order and connection of ideas is the same as the order and connection of things.”
—Baruch (Benedict)
“The rebel, unlike the revolutionary, does not attempt to undermine the social order as a whole. The rebel attacks the tyrant; the revolutionary attacks tyranny. I grant that there are rebels who regard all governments as tyrannical; nonetheless, it is abuses that they condemn, not power itself. Revolutionaries, on the other hand, are convinced that the evil does not lie in the excesses of the constituted order but in order itself. The difference, it seems to me, is considerable.”
—Octavio Paz (b. 1914)