In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are:
- the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably infinite set; and
- the set of all real numbers is an uncountably infinite set.
Read more about Infinite Set: Properties, History
Famous quotes containing the words infinite and/or set:
“Vanity is as advantageous to a government as pride is dangerous. To be convinced of this we need only represent, on the one hand, the numberless benefits which result from vanity, as industry, the arts, fashions, politeness, and taste; and on the other, the infinite evils which spring from the pride of certain nations, a laziness, poverty, a total neglect of everything.”
—Charles Louis de Secondat Montesquieu (1689–1755)
“Colleges, in like manner, have their indispensable office,—to teach elements. But they can only highly serve us, when they aim not to drill, but to create; when they gather from far every ray of various genius to their hospitable halls, and, by the concentrated fires, set the hearts of their youth on flame.”
—Ralph Waldo Emerson (1803–1882)