Is there a symbol to mean 'this is undefined'?

notation

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 $\nexists f(x)$?


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

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