Math 2.0

Concept

Equation xy = yx

Summary

In general, exponentiation fails to be commutative. However, the equation xy=yxx^y = y^x has an infinity of solutions, consisting of the line x=yx=y and a smooth curve intersecting the line at (e,e)(e,e), where ee is Euler's number. The only integer solution that is on the curve is 24=422^4=4^2.

Further reading

  1. Wikipedia, page 50167582, revision 1329494439, Equation xy = yx. adopted
About this page
Tag1HFRNREDN0
URIm2://1HFRNREDN0
Aliasesa-b-b-a, equation-x-y-y-x, equation-x-y, x-y-y-x
Kindconcept
WritingW1 stated
Same as
Changed4 November 2026

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  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

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