Função x^x não mostra o domínio correto

Louise Arreguy shared this problem 4 months ago
Not a Problem

A função x^x tem domínio em R, mas o GeoGebra mostra o domínio como R+, mesmo em -x^-x, o que mostra que o aplicativo é perfeitamente capaz de calcular a função, mas não calcula, mesmo assim.

Comments (4)

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Domain is something strange like R+ union Q- https://math.stackexchange....


(so what you see in GeoGebra is expected)

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what means x^x for x real. I know reals from Dedekind cuts for x>0 ie x=(A,B) , x^x=(Q\(B^B),B^B)

I know that the Q field is isomorphic to a subset of R for + and * but I do not know a definition of x^x for x<0 x real

I need first to define real, then operations in real then domain so I got real domain of x^x operation is R+

and for me x real and x<0 implies x^x does not exist


NOTE: I know Cauchy's successions for defining real numbers, but x^x with x<0 is not possible also

¿am I wrong?

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(-2/3)^(-2/3) = cbrt(9/4)
so OK for Q

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yes, in rational numbers

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