# Article

# Article

- Mathematics
- Arithmetic
- Subtraction

- Mathematics
- Algebra and number theory
- Subtraction

# Subtraction

Article By:

**Blumenthal, Leonard M. **Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.

Last reviewed:2014

DOI:https://doi.org/10.1036/1097-8542.664700

**One of the four fundamental operations of arithmetic and algebra.** The first printed use of the symbol − to denote subtraction is in Johann Widman's *Behennde und hüpsche Rechnung*, Leipzig, 1489. Subtraction is often regarded as an operation inverse to addition, that is, if *a* and *b* are numbers, the number *a* − *b* is defined as that number which added to *b* gives *a.* The more modern viewpoint eliminates subtraction completely by considering the number *a* − *b* as the sum of *a* and that number (denoted by −*b*) which added to *b* gives 0. The number symbolized by −*b* is called the inverse of *b* (with respect to addition). Every real number has a unique inverse (the number 0 is its own inverse) and so for each two numbers *x, y* the operation *x* + (−*y*) gives a number. Clearly,

*x*+ (−

*y*) has the property of

*x*−

*y*when subtraction is regarded as the inverse of addition. It may, then, be denoted by

*x*−

*y.*In this sense, “subtraction” may be performed on objects of many different kinds, and the original numerical operation may be greatly extended.

*See also:*

**Addition**;

**Algebra**;

**Division**;

**Multiplication**;

**Number theory**

The content above is only an excerpt.

for your institution. Subscribe

To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.

to your librarian. Recommend

Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.

## About AccessScience

#### AccessScience provides the most accurate and trustworthy scientific information available.

Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Its dedicated editorial team is led by Sagan Award winner John Rennie. Contributors include more than 9000 highly qualified scientists and 39 Nobel Prize winners.

**MORE THAN 8500** articles and Research Reviews covering all major scientific disciplines and encompassing the *McGraw-Hill Encyclopedia of Science & Technology* and *McGraw-Hill Yearbook of Science & Technology *

**115,000-PLUS** definitions from the *McGraw-Hill Dictionary of Scientific and Technical Terms *

**3000** biographies of notable scientific figures

**MORE THAN 17,000** downloadable images and animations illustrating key topics

**ENGAGING VIDEOS** highlighting the life and work of award-winning scientists

**SUGGESTIONS FOR FURTHER STUDY** and additional readings to guide students to deeper understanding and research

**LINKS TO CITABLE LITERATURE** help students expand their knowledge using primary sources of information