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Consider a partial function $f$ that is defined only for a few values of its domain (my exact use case is $\delta$ transition functions in automata). One can 'complete' it by saying $g(x)=0\iff f(x) \text{ is not defined.}$

Is there a symbol to mean "undefined"? Would it be correct, or accurate, to write $\nexists f(x)$?

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    In matrix algebra texts, $\perp$ is usually reserved for the annihilator of a matrix i.e. $(A^\perp)^T A = 0 $ and $\begin{bmatrix} A &A^\perp \end{bmatrix}$ is full rank.2011-09-04

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A language for mathematical knowledge management uses $f(x)\uparrow$.