= Domain of a partial function
For a <partial function> $f:X\rightharpoonup Y$, its <domain of a partial function> is the <subset>
$$
D=\{x\in X:f(x)\text{ is defined}\}.
$$
Its restriction to $D$ is an ordinary <function> $D\to Y$. Outside $D$, <function evaluation> has no assigned value.
For instance, the real <square root> as a <partial function> on the <real line> has $D=[0,\infty)$. Both $0$ and $-1$ lie in the surrounding source, but only at zero is there an output; the value zero and absence of a value are different situations.
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