Skip to main content
Select Source:

Integers

Integers


Integers are the set of numbers {, 4, 3, 2, 1, 0, 1, 2, 3, 4, } that encompass the counting numbers, {1, 2, 3, }, the negative of the counting numbers, { 3, 2, 1} and zero. Integers can be shown on a simple number line.

The integers on the left side of zero (0) are called negative numbers, and are represented by a negative sign () placed before them, as in 5, 10, and 15.* The integers on the right side of 0 are called positive numbers. Examples include 5, 10, and 15. The positive integers are known as counting numbers or natural numbers. The positive integers and 0 are called whole numbers. Zero is an integer but it is neither positive nor negative.

*Some historians believe the first evidence of the use of negative numbers was around 300 b.c.e. in China.

Integers are used in everyday life. A debt or a loss is often expressed with a negative integer. A gain is usually expressed with a positive integer. When the temperature is warmer than the zero point of the temperature scale, it is represented with a positive sign; when it is colder than the zero point, it is represented with a negative sign.

see also Numbers, Real; Numbers, Whole; Zero.

Marzieh Thomasian

Bibliography

Aufmann, Richard N., and Vernon C. Baker. Basic College Mathematics, 4th ed. Boston: Houghton Mifflin Company, 1991.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Integers." Mathematics. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"Integers." Mathematics. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/education/news-wires-white-papers-and-books/integers

"Integers." Mathematics. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/education/news-wires-white-papers-and-books/integers

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integer Any negative or positive whole number or zero, e.g. … −3, −2, −1, 0, 1, 2, 3 … There are a limitless (infinite) number of integers. The positive integers are the natural numbers. The existence of negative integers and zero allow any integer to be subtracted from any other integer to give an integer result.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." World Encyclopedia. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." World Encyclopedia. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/integer

"integer." World Encyclopedia. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/integer

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integer XVI. — L. integer intact, ENTIRE.
So integral making up a whole, made up of parts XVI; (math.) XVIII. — late L. integrālis. integrate XVII. f. pp. stem of L. integrāre. integration XVII. — L. integrity XV. — F. or L.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-2

"integer." The Concise Oxford Dictionary of English Etymology. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-2

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integer a whole number; a number which is not a fraction. The word is recorded from the early 16th century, as an adjective meaning ‘entire, whole’, and comes from Latin, ‘intact, whole’.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." The Oxford Dictionary of Phrase and Fable. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." The Oxford Dictionary of Phrase and Fable. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer

"integer." The Oxford Dictionary of Phrase and Fable. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integer A whole number, as opposed to a rational or real number. The concept of integer type is used for computer representation of a finite subset of the integers.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." A Dictionary of Computing. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." A Dictionary of Computing. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/integer

"integer." A Dictionary of Computing. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/integer

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

in·te·ger / ˈintijər/ • n. 1. a whole number; a number that is not a fraction. 2. a thing complete in itself.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-1

"integer." The Oxford Pocket Dictionary of Current English. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-1

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integer: see number; number theory.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/integer

"integer." The Columbia Encyclopedia, 6th ed.. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/integer

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.

integer

integerbadger, cadger •Alger, neuralgia •ganja, grandeur, phalanger •charger, enlarger, maharaja, raja •slàinte • turbocharger •dredger, edger, hedger, ledger, pledger, St Leger •avenger, revenger •gauger, golden-ager, major, old-stager, pager, rampager, sergeant major, stager, wager •arranger, changer, danger, endanger, exchanger, Grainger, hydrangea, manger, ranger, stranger •moneychanger • teenager •bushranger •besieger, paraplegia, procedure •abridger •cringer, ginger, impinger, infringer, injure, ninja, whinger, winger •dowager • voyager • harbinger •bondager • wharfinger • packager •Scaliger •challenger, Salinger •pillager, villager •armiger • scrimmager •rummager, scrummager •manager • derringer • forager •porringer • encourager •Massinger, passenger •presager • messenger • Kissinger •integer, vintager •cottager • frontager • ravager •salvager • scavenger •Elijah, Niger, obliger •codger, dodger, lodger, roger, todger •forger, Georgia, gorger •gouger •lounger, scrounger •sunlounger • soldier •Abuja, puja

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"integer." Oxford Dictionary of Rhymes. . Encyclopedia.com. 20 Feb. 2018 <http://www.encyclopedia.com>.

"integer." Oxford Dictionary of Rhymes. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-0

"integer." Oxford Dictionary of Rhymes. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/integer-0

Learn more about citation styles

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 most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

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.