 Essential variable of a function

A coordinate of a function on a finite Cartesian product is essential if changing that coordinate, with all the others fixed suitably, can change the output. A coordinate is inessential precisely when such a change never affects the output in any context. If only coordinate $i$ is essential, changing the other coordinates one at a time proves that the output is $g(x_i)$ for a nonconstant unary function $g$. This deterministic dependence definition is not by itself a probabilistic or experimental notion of causal inference.