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@atheist nope, 0^-1 aka 1/0 is undefined. It can be anything from negative infinity to positive infinity.
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atheist99863y@Lensflare *engage nerd mode*
I prefer the argument it's +/- infinity, I get the logic of what you're saying, a/0=x, ergo x*0=a and so any valid combination of numbers gives any valid results. Although I prefer the limit result as it generalizes better, eg the complex plane can be considered a sphere, tan(x) is a valid continuous function in that case and its possible to go from 1 to - 1 in a straight line without passing through 0 (there's other weirdness supporting this, stuff like circle projection, but I'd need to go find notes, it's been a decade since I did complex analysis) -
@atheist yes, the limit can be considered +/- infinity but thats not useful.
But interesting to think about. -
atheist99863y@Lensflare my point is it is useful in complex math (imaginary numbers) which shows up all over the place. Including in real numbers, eg trig equations are easier to simplify using complex identities.
5x6 = 30
4x8 = 32
rant