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).

Domain, Codomain, and Image