I need help to classify this number. The solutions to $3^y-y^3=0$ are 3 and 2.47805268.... it is irrational But since it is a root for this equation is the number transcedental or not? The original problem comes from $3^y=y^3$ where one sees it is an irrational number.
2026-03-25 12:46:10.1774442770
Transcedental number or not?
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By the Gelfond-Schneider theorem, if $y$ is an algebraic irrational then $3^y$ is transcendental, but $y^3$ is algebraic, therefore they can't be equal.