Largest x, x^2 less than 2Date: 10/23/1999 at 08:16:58 From: Michael Subject: Logic Dear Dr. Math, Could you please assist me with the following question: Prove that there is no largest real number x, such that x^2 < 2. (Use indirect proof.) Thanking you in advance, Michael Date: 10/25/1999 at 02:22:35 From: Doctor Floor Subject: Re: Logic Hi, Michael, Thanks for your question. Suppose that x is the largest x such that x^2 < 2. Then x < sqrt(2) Let y = [x+sqrt(2)]/2 then x < y < sqrt(2) and y^2 < 2 And we have a contradiction. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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