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INFINITY, FINITE SETS AND INFINITE SETS


 

Infinity is a term commonly used to refer to a quantity or distance that is so large it cannot be counted or measured. In mathematics, the idea of infinity forms an important part of set theory.

A set of objects or numbers is called finite if the objects or numbers can be paired with the positive integers (whole numbers) less than some positive integer. For example, a set of playing cards of one suit, which consists of 13 members, is finite. The cards can be paired with the positive integers less than 14.

An infinite set is defined as one that is not finite. Its members cannot be paired with the positive i ntegers less than some positive integer, because the set continues without end. For example, the set of all positive integers--1, 2, 3, 4, and so on--is infinite, as is the set of all fractions. Both sets have an unlimited number of members.Infinite sets may be represented by placing three dots after the last member noted. For example, the set of even numbers above zero may be written 2, 4, 6...

The idea of infinity has other applications in mathematics in addition to set theory. In projective geometry, for example, the point at infinity is defined as the intersection of all parallel lines.

 

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