# S32 - [IMAGE Admittedly it takes as much work to show that[IMAGE is irrational as that e is irrational Postscript After posting the solution above

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Solution to Problem 32 Congratulations to this week’s winners Mike Fitzpatrick, Ryan Vaughan, and Tim Parks Correct solutions were also received from Abhi Dattasharma, Andreas Low, Yang Lu, Murat Ozkan, Bill Rosenberg, BHActuary, and Sid. All solutions but one offered [IMAGE] , or some slight variation on this theme. Although the solution is certainly correct, the mathematician in me needs to point out that it requires some substantial mathematics to show that either e or ln(2) is irrational. The solution sent in by Abhi Dattasharma was really sweet. Appropriately, he says saw the answer in [IMAGE] seconds! Here it is:

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Unformatted text preview: [IMAGE] Admittedly, it takes as much work to show that [IMAGE] is irrational as that e is irrational. *** Postscript: After posting the solution above, I received two improvements based on Dattasharma’s solution and requiring no substantial mathematical knowledge. The first came from Thomas Teo. He observes that if [IMAGE] is irrational, then Dattasharma’s solution will suffice. On the other hand if that number is rational, that makes [IMAGE] irrational which when raised to the power of [IMAGE] will do the trick. Jan Siwanowicz offered a similar improvement. this page....
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## This note was uploaded on 03/01/2010 for the course MATH 301 taught by Professor Albertodelgado during the Spring '10 term at Bradley.

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S32 - [IMAGE Admittedly it takes as much work to show that[IMAGE is irrational as that e is irrational Postscript After posting the solution above

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