User Name Remember Me? Password

 Math General Math Forum - For general math related discussion and news

 March 9th, 2015, 06:27 PM #1 Newbie   Joined: Mar 2015 From: Lake Placid Posts: 2 Thanks: 0 proof of Irrationality of e I'm an AP Calc BC student. We just learned Euler's way to prove the irrationality of e. I just suddenly came up with this weird proof in class. But I couldn't find anything wrong with it. Can you guys check this proof and point out any mistake hopefully? Thanks a lot! if e is rational, then e=m/n(simplest form), where m,n are unequal integers(n is not 0) then ln(e)=ln(m/n) then 1=ln(m/n)=logn(m) that turns out m=n, which is not true and also contradicted to "m,n are unequal integers" then e is irrational. March 9th, 2015, 06:47 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 Are you saying $\displaystyle \ln\left(\frac{m}{n}\right)=\log_n{m}$ ? If so, that isn't true ... $\displaystyle \ln\left(\frac{m}{n}\right) \ne \frac{\ln{m}}{\ln{n}}=\log_n{m}$ $\displaystyle \ln\left(\frac{m}{n}\right) = \ln{m}-\ln{n}$, remember? March 10th, 2015, 03:47 AM #3 Newbie   Joined: Mar 2015 From: Lake Placid Posts: 2 Thanks: 0 Thanks a lot. I misused the change base formula Tags irrationality, proof Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Roli Algebra 0 May 2nd, 2014 10:22 AM Eureka Number Theory 10 October 27th, 2011 05:47 PM clandarkfire Algebra 4 May 14th, 2011 09:06 PM jstarks4444 Number Theory 1 May 5th, 2011 03:18 PM symrikol Number Theory 1 September 29th, 2008 08:09 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.      