By the definition of an algebraic structure $(X,\ast),$ the image of the binary operation is a subset of $X,$ formally $\ast[X,X]\subseteq X$. We express this property by saying that $X$ is closed under the operation "$\ast$".
Axioms: 1 2 3 4
Chapters: 5 6 7 8
Definitions: 9
Explanations: 10 11
Motivations: 12 13
Proofs: 14