**Infinity** (symbol: ∞) refers to something *without any limit*, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word *infinity* derives from Latin *infinitas*, which can be translated as "unboundedness", itself derived from the Greek word *apeiros*, meaning "endless".

In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite.

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### Famous quotes containing the word infinity:

“As we begin to comprehend that the earth itself is a kind of manned spaceship hurtling through the *infinity* of space—it will seem increasingly absurd that we have not better organized the life of the human family.”

—Hubert H. Humphrey (1911–1978)

“The poetic notion of *infinity* is far greater than that which is sponsored by any creed.”

—Joseph Brodsky (b. 1940)

“We must not suppose that, because a man is a rational animal, he will, therefore, always act rationally; or, because he has such or such a predominant passion, that he will act invariably and consequentially in pursuit of it. No, we are complicated machines; and though we have one main spring that gives motion to the whole, we have an *infinity* of little wheels, which, in their turns, retard, precipitate, and sometime stop that motion.”

—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)