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

Question

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 $\nexists f(x)$?

I remember $\bot$ being used. See http://en.wikipedia.org/wiki/Partial_function#Bottom_type. — Srivatsan, Sep 04 '11 at 21:59
@Srivatsan You mean, $f(x) = \bot$? I remember something of the sort. — badp, Sep 04 '11 at 22:09
Ah yes. I meant $f(x) = \bot$. (But this is just what I remember, so not to be trusted. Hopefully some expert can corroborate.) — Srivatsan, Sep 04 '11 at 22:10
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. — , Sep 04 '11 at 23:01

Charles · Accepted Answer · 2019-03-06T13:22:21.993

16

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

edited Mar 06 '19 at 13:22

answered Sep 05 '11 at 02:39

Charles

32,122

2

I had not seen this before, but I have seen $f(x) \downarrow$ to mean that $f(x)$ is defined, so this makes sense. – Toby Bartels Jan 22 '16 at 19:19
The link you provided is dead :( – exhuma Mar 06 '19 at 09:44
@exhuma I replaced it with a more stable link. – Charles Mar 06 '19 at 13:22
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I think you will loose more readers using this symbol rather than not using it and writing in plain text. From what I have seen on this site purely logical symbols are not commonly used except in this field (logic) and the large majority of people replace them by plain text (and/or for instance are almost never replaced by $\land,\lor$ in general math). – zwim Apr 19 '20 at 21:22

score 0 · Answer 2 · answered Sep 10 '23 at 18:41

Thus, $f(x)\uparrow$ and $f(x)=\bot$ were suggested, although the prior use of the latter is perhaps not common (I did not quickly find it from Google).

$f(x)=\frac00$ might suit some contexts.

I would use none of the above without defining it first.

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

2 Answers2

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