Binary operation: Difference between revisions
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==Definition== | ==Definition== | ||
A [[binary operation]] on a set <math>X</math> is a function <math>\ast: X \times X \to X</math>. | A [[binary operation]] on a set <math>X</math> is a function <math>\ast: X \times X \to X</math>. | ||
==Examples== | |||
* Addition is a binary operation on the integers, rational numbers, real numbers and complex numbers. | |||
* Matrix multiplication is a binary operation on the set of <math>n \times n</math> matrices for any <math>n</math>. | |||
==In abstract algebra== | |||
A [[group]] is a set equipped with a binary operation that has an identity element, an inverse for each element, and associativity. | |||
Latest revision as of 19:40, 13 January 2024
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition
A binary operation on a set is a function .
Examples
- Addition is a binary operation on the integers, rational numbers, real numbers and complex numbers.
- Matrix multiplication is a binary operation on the set of matrices for any .
In abstract algebra
A group is a set equipped with a binary operation that has an identity element, an inverse for each element, and associativity.