ok actually it's poll time

f^-2 (a) =

@lina notation abuse. (f^{-1}(x)) and (f^2(x)) are common enough that you can get away with exactly those two meaning inverse function and squared output of function. but any other exponent is unacceptable. you have to clarify what you mean or else this is meaningless

@sodiboo @lina sodi^πi(boo)

@sodiboo @lina it is unacceptable and you will be receiving a letter from my lawyer if I see you’ve written a paper that uses f^3(x)

@KaitlynEthylia @lina (f^3(x)) is pushing the line. it and the next few positive integers are simple enough that they can’t mean anything other than “the same operation as (f^2(x)) but with a new argument”. but they’re uncommon enough that this isn’t an obvious truth.

it’s perhaps not absolutely meaningless without clarification. but these are still definitely notation abuse. just slightly less so than (f^{-2}(x)).

@sodiboo @lina I mean i'm still convinced that f²(x) as output squared is notation abuse. Without clarification, unless obvious from context, it reads to me (and evidently a lot of other people too) as repeated application

@KaitlynEthylia @lina oh yeah I’m not trying to defend the common forms of (f^{-1}(x)) and (f^2(x)). their coexistence is also notation abuse, even if generally well understood.

but I’m saying that the cooked up case of (f^{-2}(x)) (and to a lesser extent, basically any other exponent) is notation abuse and little of anything else. it’s notation abuse for the sake of notation abuse. therefore it’s meaningless (see also: the fact that the poll has to exist in the first place).