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Is there a mathematical symbol that lets me say something like "5 is in the domain of f" or "5 is NOT in the domain of f"?

CoilKid
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2 Answers2

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$x \in \text{dom} \ f$, $x \notin \text{dom} \ f$

In your case, we'd have $x=5$.

MathematicsStudent1122
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  • I just used that as a simplified example. My actual problem is something like "$0 \text{ not in the domain of } x^{2}+1$" I think "$0 \notin \text{dom } x^2 +1$" should work quite well, unless you can't use the notation with an equation. – CoilKid Sep 21 '16 at 20:28
  • Well, $x^2 + 1$ is not a function. It's an expression. Talking about the domain of $x^2 + 1$ makes no sense. – MathematicsStudent1122 Sep 21 '16 at 20:35
  • I just realized I was looking for the wrong thing... Dangit. $\text{dom}$ will be handy in future, but I really need something for "0 not in the solution set of"... Also, I should be more careful with my wording. "Expression" and "equation" mean different things when speaking mathematically. – CoilKid Sep 21 '16 at 20:35
  • You answered this particular question quite nicely though. Thanks! – CoilKid Sep 21 '16 at 20:36
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In computability theory the notation $f(x)\downarrow$ is often used for $x \in dom(f)$. The terminology that is used in this context is that the computation of $f(x)$ converges. The corresponding notation for $x \not \in dom(f)$ is $f(x) \uparrow$. I rather like this notation but it is seldom encountered outside of computability theory

John Coleman
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