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Using negative powers for applications of the inverse function is arguably consistent, because it is a generalization of the same notation for linear maps. It
by enriquto 6y ago
Using negative powers for applications of the inverse function is arguably consistent, because it is a generalization of the same notation for linear maps.
It does not pose major problems, either. You can easily distinguish f^p(x) and f(x)^p. The first one means "apply f p times to x, iteratively" and the second one means "compute f(x) and raise it to p". It works just as well when p=-1.
- BeetleB 6y ago> Using negative powers for applications of the inverse function is arguably consistent, because it is a generalization of the same notation for linear maps. Except that no one will let you get away with (sin^-1)^-1 x to represent sin x. But you can do that with inverse function notation in general. Some of this is just cultural.
- enriquto 6y agoThat would be a strange notation indeed. But I once met an engineer that called the exponential function the "antilogarithm". It was not a weird mannerism, it was his bona-fide way of calling the function exp(x). Apparently it was the standard name where he came from (somewhere in south america).
- BeetleB 6y agoI've seen antilogarithm in textbooks. I think it's more common in the complex domain.