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Is it true that in some cases an irrational number raised to a rational power is rational? If so what kinds of irrational numbers?
A very simple example is ##\pi^0 = 1##.Is it true that in some cases an irrational number raised to a rational power is rational? If so what kinds of irrational numbers?
Note that the irrational number has to be algebraic. A transcendental number raised to a rational power cannot be rational. In fact, it must still be transcendental.
Isn't there a contradiction here?A very simple example is ##\pi^0 = 1##.
##\pi## is irrational, and 0 is rational.
I think you just became a candidate for the Fields medal!Isn't there a contradiction here?
No , I just became the candidate for another coffee!I think you just became a candidate for the Fields medal!
That was arildno...No , I just became the candidate for another coffee!
Sorry Mark44, completely missed your humor there...
I thought you were trying to be funny by proposing the trivial case "to the power of 0".That was arildno...