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)
“Fruits are acceptable gifts, because they are the flower of commodities, and admit of fantastic values being attached to them. If a man should send to me to come a hundred miles to visit him, and should set before me a basket of fine summer-fruit, I should think there was some proportion between the labor and the reward.”
—Ralph Waldo Emerson (1803–1882)