#infinity

Infinity

from Britannica

infinity, the concept of something that is unlimited, endless, without bound. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical.

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless.

One of the earliest appearances of infinity in mathematics occurs in regards the ratio between the diagonal and the side of a square. The diagonal and the side of a square are incommensurable—that is, their lengths cannot both be expressed as whole-number multiples of any shared unit. The ratio is irrational and that it is the limit of an endless, nonrepeating decimal series. the general Greek abhorrence of the notion of infinity. Aristotle influenced subsequent thought for more than a millennium with his rejection of “actual” infinity (spatial, temporal, or numerical), which he distinguished from the “potential” infinity of being able to count without end. To avoid the use of actual infinity, Eudoxus of Cnidus (c. 400–350 bce) and Archimedes (c. 285–212/211 bce) developed a technique, later known as the method of exhaustion, whereby an area was calculated by halving the measuring unit at successive stages until the remaining area was below some fixed value (the remaining region having been “exhausted”).

Infinity

from Standford Encyclopedia of Philosophy

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