What does it mean when a function is set to zero?

Question

I am reading an article about the Reproduction numbers and I found the next phrase:

• If $\mathcal{F}(x)$ is set to zero, then all eigenvalues of $Df (x)$ have negative real parts.

and my question is what does it mean that a function is set to zero.

Answer 1

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 $ f^{-1}(0)$, the inverse image of $\{0\}$ in $X$.