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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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    Some people write $f(x)\uparrow$.2011-09-04
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    I remember $\bot$ being used. See http://en.wikipedia.org/wiki/Partial_function#Bottom_type.2011-09-04
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    However $\not\exists f(x)$ seems confusing though.2011-09-04
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    @Srivatsan You mean, $f(x) = \bot$? I remember something of the sort.2011-09-04
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    Ah yes. I meant $f(x) = \bot$. (But this is just what I remember, so not to be trusted. Hopefully some expert can corroborate.)2011-09-04
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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 $f(x)\uparrow$.

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    I had not seen this before, but I have seen $f(x) \downarrow$ to mean that $f(x)$ *is* defined, so this makes sense.2016-01-22