Actual Infinity

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:

    That the mere matter of a poem, for instance—its subject, its given incidents or situation; that the mere matter of a picture—the actual circumstances of an event, the actual topography of a landscape—should be nothing without the form, the spirit of the handling, that this form, this mode of handling, should become an end in itself, should penetrate every part of the matter;Mthis is what all art constantly strives after, and achieves in different degrees.
    Walter Pater (1839–1894)

    New York, you are an Egypt! But an Egypt turned inside out. For she erected pyramids of slavery to death, and you erect pyramids of democracy with the vertical organ-pipes of your skyscrapers all meeting at the point of infinity of liberty!
    Salvador Dali (1904–1989)