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August 11th, 2019, 10:09 PM  #1 
Newbie Joined: Aug 2019 From: India Posts: 2 Thanks: 0  Real analysis rudin theorem 1.21
In thorem 1.21 of Rudin He has said that as t=X/(X+1) then t^n<t<1 then maximum value of t is 1. then in the next part he has given that t^n<t<x. as maximum value of t is less than 1 why has he given that t<x ? X is a real number and 0<X and And n Is a integer n>0 . 
August 11th, 2019, 10:32 PM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 927 Math Focus: Wibbly wobbly timeywimey stuff. 
Please don't double post. Dan 
August 12th, 2019, 12:24 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
The image is much too fuzzy to read.

August 12th, 2019, 05:23 AM  #4 
Senior Member Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 
X is positive, so (X+1) > 1. Dividing a positive number by something greater than one makes it smaller, so t = X/(X+1) must be less than X.


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