Can You Solve x^x^x^... = 2? Infinite Exponent Tower Trick

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  • Published on:  Sunday, December 28, 2014
  • What is the value of this infinite exponent tower?

    See my follow-up video about a potential paradox 4 = 2:
    https://www.faceclips.net/video/DmP3sFIZ0XE/video.html

    I was asked this problem in a high school math competition, and you had to solve it as fast as possible. Hence I made a short 1 minute video showing this trick. For those wanting a proof suitable for a graduate level real analysis course (which is the only way to rigorously approach this problem), here are references.

    Award winning paper Knoebel, R. Arthur. "Exponentials reiterated." The American Mathematical Monthly 88.4 (1981): 235-252.
    http://www.maa.org/programs/maa-awards/writing-awards/exponentials-reiterated-0

    Direct link to pdf:
    https://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf

    Wikipedia tetration
    https://en.wikipedia.org/wiki/Tetration#Extension_to_infinite_heights

    False proof 2 equals 4
    https://jeremykun.com/2012/05/05/false-proof-2-4-as-the-limit-of-an-infinite-power-tower/

    Math StackExchange links
    https://math.stackexchange.com/questions/87870/are-these-solutions-of-2-xxx-cdot-cdot-cdot-correct/87897#87897
    https://math.stackexchange.com/questions/108288/infinite-tetration-convergence-radius?rq=1

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  • Source: https://youtu.be/JrOG1tKAatg
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