First of all, we want to define formally, what exactly shall be understood under an algebraic structure. We start with the concept of a *binary operation*.

**Definition**: Binary Operation

A **binary operation** \(\ast\) on a set \(X\) ist a total function $\ast :X\times X\to X$ mapping all pairs $x,y\in X\times X$ to a specific $z\in X,$ formally $$x\ast y:=\ast (x,y)=z.$$

| | | | | created: 2016-09-04 19:02:19 | modified: 2019-02-05 23:16:30 | by: *bookofproofs* | references: [6907]

### CC BY-SA 3.0

[6907] **Brenner, Prof. Dr. rer. nat., Holger**: “Various courses at the University of OsnabrÃ¼ck”, https://de.wikiversity.org/wiki/Wikiversity:Hochschulprogramm, 2014

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