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Encyclopedia—number

The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their members can be matched in a one-to-one correspondence. Ordinal numbers refer to position relative to an ordering, as first, second, third, etc. The finite cardinal and ordinal numbers are called the natural numbers and are represented by the symbols 1, 2, 3, 4, etc. Both types can be generalized to infinite collections, but in this case an essential distinction occurs that requires a different notation for the two types (see transfinite number).

Sections in this article:

Introduction
The Natural Numbers
The Integers and Rational Numbers
The Real Numbers
The Complex Numbers
The Algebraic and Transcendental Numbers
Bibliography

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2007, Columbia University Press. All rights reserved.

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