Real analysis Rudin theorem 1.21

Darshan

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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 ?
 

Dr.Peterson

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This is very terse (and I don't have access to a list of theorems already proved), so we can't be sure of all the reasoning; but perhaps he concludes that t < x because x is being divided by 1+x, which is greater than 1. It is not derived from t < 1.
 

pka

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View attachment 13209

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 ?
Here is a LINK that discusses this problem..
 
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