"shorthand notation" for $x^{-1}$

Question

I had a student write "$x^-$" as a "shorthand" for $x^{-1}$. Is anyone aware of a context where this is standard notation?

Edit: Since it appears that as far as anyone knows he did just make it up, it seems unlikely that anyone will ever have the same question. Hence I was planning on deleting the question. It's been suggested that I shouldn't delete it after it's been answered. Fine.

I may as well add this, so a reader might get something out of reading the question: I marked it wrong with a big question mark. He asked what the question was, I said I had no idea what $x^--$ meant, he said it was shorthand for $x^{-1}$.

[insert pause; timing...] So I told him his score of 40/50 was shorthand for 50/50.[rim shot]

Answer 1

I don't think it should be accepted, but I have an idea why a student may have made it up.

In chemistry it is standard to write for example $Cl^-$, whereas for higher charging states numbers are usually added, e.g. $P^{2-}$, $P^{3-}$ etc; although I have also seen things like $P^=$ instead of $P^{2-}$. But when charge is only 1 e, the number is never written i.e. always $Cl^-$ never $Cl^{1-}$ and certainly not $Cl^{-1}$.

Of course ion charge states are completely different from mathematical exponentiation. They both just happen to use superscripts; and in chemistry these are symbols, not numbers.

Answer 2

I do not believe this is standard notation.

The only place where I have seen a superscript minus sign is in contexts where we're interested in separating a function into its positive and negative parts (e.g. in Lebesgue integration).

Specifically, given $f : X \to \mathbb{R}$, define $$f^+(x) = \begin{cases} f(x) & \text{if } f(x) \ge 0 \\ 0 & \text{otherwise} \end{cases} \quad \text{and} \quad f^-(x) = \begin{cases} -f(x) & \text{if } f(x) \le 0 \\ 0 & \text{otherwise} \end{cases}$$

Then $f^+$ and $f^-$ are non-negative-valued and $f = f^+ - f^-$.

Obviously this has nothing to do with the reciprocal or inverse, but I thought I'd add it because I didn't think "I do not believe this is standard notation" was worthy of an answer on its own.