Natural Numbers (Encyclopedia of Science)
The natural numbers are the ordinary numbers, 1, 2, 3, etc., with which we count. They are sometimes called the counting numbers. They have been called natural because much of our experience from infancy deals with discrete (separate; individual; easily countable) objects such as fingers, balls, peanuts, etc. German mathematician Leopold Kronecker (1823891) is reported to have said, "God created the natural numbers; all the rest is the work of man."
Some disagreement exists as to whether zero should be considered a natural number. One normally does not start counting with zero. Yet zero does represent a counting concept: the absence of any objects in a set. To resolve this issue, some mathematicians define the natural numbers as the positive integers. An integer is a whole number, either positive or negative, or zero.
Operations involving natural numbers
Ultimately all arithmetic is based on the natural numbers. When multiplying 1.72 by .047, for example, the multiplication is done with the natural numbers 172 and 47. Then the result is converted to a decimal fraction by inserting a decimal point in the proper place. The placement of a decimal point is also done by counting natural numbers. When adding the fractions 1/3 and 2/7, the process is also one that involves natural numbers. First, the fractions are converted to 7/21 and 6/21. Then, the...
(The entire section is 390 words.)
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