Zero set

Zero set

In various areas of mathematics, the zero set of a function is the set of all its zeros. More precisely, if ${\displaystyle f:X\to \mathbb {R} }$ is a real-valued function (or, more generally, a function taking values in some additive group), its zero set is ${\displaystyle f^{-1}(0)}$, the inverse image of ${\displaystyle \{0\}}$ in ${\displaystyle X}$.