Infinity

Infinity (symbol: ∞) is an abstract concept describing something without any bound or larger than any number. Philosophers have speculated about the nature of the infinite, such as Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. Modern mathematics uses the concept of infinity in the solution of many practical and theoretical problems, such as in calculus and set theory, and the idea also is used in physics and the other sciences.

In mathematics, "infinity" is often treated as a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as natural or real numbers.

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 infinite set of real numbers is uncountable.

Ancient cultures had various ideas about the nature of infinity. The ancient Indians and Greeks did not define infinity in precise formalism as does modern mathematics, and instead approached infinity as a philosophical concept.

The earliest recorded idea of infinity comes from Anaximander, a pre-Socratic Greek philosopher who lived in Miletus. He used the word which means infinite or limitless. However, the earliest attestable accounts of mathematical infinity come from Zeno of Elea (c. 490 BCE? – c. 430 BCE?), a pre-Socratic Greek philosopher of southern Italy and member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, described by Bertrand Russell as "immeasurably subtle and profound".

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