{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-572d6a42.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-f4d0de30.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Can You Solve x^x^x^... = 2? Infinite Exponent Tower Trick' data-url='/boclips/videos/5c6705777bf801000181579d' data-video-url='/boclips/videos/5c6705777bf801000181579d' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nCan You Solve x^x^x^... = 2? Infinite Exponent Tower Trick\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356011\" href=\"/search?publisher_ids%5B%5D=30356011\"\u003eCurated Video\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eWhat is the value of this infinite exponent tower? See my follow-up video about a potential paradox 4 = 2 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...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eWhat is the value of this infinite exponent tower? See my follow-up video about a potential paradox 4 = \u003ca href='https://www.youtube.com/watch?v=DmP3sFIZ0XE' target='_blank' rel='nofollow'\u003e2\u003c/a\u003e 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-\u003ca href='http://www.maa.org/programs/maa-awards/writing-awards/exponentials-reiterated-0' target='_blank' rel='nofollow'\u003e252.\u003c/a\u003e Direct link to \u003ca href='https://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf' target='_blank' rel='nofollow'\u003epdf\u003c/a\u003e Wikipedia \u003ca href='https://en.wikipedia.org/wiki/Tetration#Extension_to_infinite_heights' target='_blank' rel='nofollow'\u003etetration\u003c/a\u003e False proof 2 equals \u003ca href='https://jeremykun.com/2012/05/05/false-proof-2-4-as-the-limit-of-an-infinite-power-tower/' target='_blank' rel='nofollow'\u003e4\u003c/a\u003e Math StackExchange \u003ca href='https://math.stackexchange.com/questions/87870/are-these-solutions-of-2-xxx-cdot-cdot-cdot-correct/87897#87897' target='_blank' rel='nofollow'\u003elinks\u003c/a\u003e \u003ca href='https://math.stackexchange.com/questions/108288/infinite-tetration-convergence-radius?rq=1' target='_blank' rel='nofollow'\u003e\u003c/a\u003e If you like my videos, you can support me at \u003ca href='https://www.patreon.com/mindyourdecisions' target='_blank' rel='nofollow'\u003ePatreon\u003c/a\u003e Connect on social media. 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