Monday, July 29, 2019

What is wrong in this proof that pi=2 or x=2?



Let us consider the number πππ=πππ=ππ2



As the bases are equal, the exponents must be equal, So π=2




You can take any x instead of π.



What is wrong in this proof?


Answer



Lets write ab to mean ab.



Then the following reasoning is correct: (ππ)π=π(ππ)=π(π2)



However, we cannot necessarily deduce that the RHS equals




(ππ)2



because exponentiation isn't associative. Indeed, Google calculator tells me that:




  • π(π2)80662.6659386


  • (ππ)21329.48908322





so if the calculator is correct to even the first decimal place, then



(ππ)2π(π2).



Moral of the story: if in doubt, find better notation!


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