# Domain (of a function)

The do­main $$\operatorname{dom}(f)$$ of a func­tion $$f : X \to Y$$ is $$X$$, the set of valid in­puts for that func­tion. For ex­am­ple, the do­main of $$+$$ is the set of all pairs of num­bers, and the do­main of the di­vi­sion op­er­a­tion is the set of all pairs $$(x, y)$$ of num­bers where $$y$$ is non-zero.

Vi­su­al­iz­ing a func­tion as a map that takes ev­ery point in an in­put set to one point in an out­put set, the do­main is the in­put set (pic­tured on the left in red in the image be­low).

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