Actual infinity is the idea that numbers, or some other type of mathematical object, can form an actual, completed totality; namely, a set. Hence, in the philosophy of mathematics, the abstraction of actual infinity involves the acceptance of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given objects.
Read more about Actual Infinity: Aristotle's Potential–actual Distinction, Opposition From The Intuitionist School, History, Scholastic Philosophers, Classical Set Theory
Famous quotes containing the words actual and/or infinity:
“There is something else which has the power to awaken us to the truth. It is the works of writers of genius.... They give us, in the guise of fiction, something equivalent to the actual density of the real, that density which life offers us every day but which we are unable to grasp because we are amusing ourselves with lies.”
—Simone Weil (19091943)
“As we begin to comprehend that the earth itself is a kind of manned spaceship hurtling through the infinity of spaceit will seem increasingly absurd that we have not better organized the life of the human family.”
—Hubert H. Humphrey (19111978)