Natural Numbers
Natural numbers
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 (1823–1891) 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 numerators are added using naturalnumber arithmetic, and the denominators copied. Even computers and calculators reduce their complex and lightningfast computations to simple steps involving only natural numbers.
Measurements, too, are based on the natural numbers. In measuring an object with a meter stick, a person relies on the numbers printed near the centimeter marks to count the centimeters but has to physically count the millimeters (because they are not numbered). Whether the units are counted mechanically, electronically, or physically, the process is still one of counting, and counting is done with the natural numbers.
Number theory
One branch of mathematics concerns itself exclusively with the properties of natural numbers. This branch is known as number theory. Since the time of the ancient Greeks, mathematicians have explored these properties for their own sake and for their supposed connections with the supernatural. Most of this early research had little or no practical value. In recent times, however, many practical uses have been found for number theory. These include checkdigit systems, secret codes, and other uses.
[See also Arithmetic; Fraction, common; Number theory ]
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Natural Numbers." UXL Encyclopedia of Science. . Encyclopedia.com. 19 Apr. 2018 <http://www.encyclopedia.com>.
"Natural Numbers." UXL Encyclopedia of Science. . Encyclopedia.com. (April 19, 2018). http://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/naturalnumbers
"Natural Numbers." UXL Encyclopedia of Science. . Retrieved April 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/science/encyclopediasalmanacstranscriptsandmaps/naturalnumbers
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
natural numbers
nat·u·ral num·bers • pl. n. the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"natural numbers." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 19 Apr. 2018 <http://www.encyclopedia.com>.
"natural numbers." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (April 19, 2018). http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/naturalnumbers
"natural numbers." The Oxford Pocket Dictionary of Current English. . Retrieved April 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/naturalnumbers
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.