# 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.

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