In general, exponentiation fails to be commutative. However, the equation x y = y x {\displaystyle x^{y}=y^{x}} has an infinity of solutions, consisting of the line x = y {\displaystyle x=y} and a smooth curve intersecting the line at ( e , e ) {\displaystyle (e,e)} , where e {\displaystyle e} is Euler's number.
In general, exponentiation fails to be commutative. However, the equation x y = y x {\displaystyle x^{y}=y^{x}} has an infinity of solutions, consisting of the line x = y {\displaystyle x=y} and a smooth curve intersecting the line at ( e , e ) {\displaystyle (e,e)} , where e {\displaystyle e} is Euler's number.
Source: Wikipedia "Equation xy = yx" · CC BY-SA 4.0
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