Unital magma

A magma $(M,*)$ is said unital if there exists an element $e\in M$ , called identity element, such that for all $x\in M$ :
$x*e=x=e*x.$

$\bullet$ If $(M,*)=(\Z,+)$ , then $e=0$ .
$\bullet$ If $(M,* )=(\R^*,\cdot)$ then $e=1$ .

Practice this concept with exercises

Let $(M,*)$ be a unital magma with identity element $e$ . Show that $e$ is unique.

Open exercise

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