Why is an Upper Bound for in Theorem 3.47?

  • #1
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I am reading Karl R. Stromberg's book: "An Introduction to Classical Real Analysis". ... ...

I am focused on Chapter 3: Limits and Continuity ... ...

I need further help in order to fully understand the proof of Theorem 3.47 on page 107 ... ... Theorem 3.47 and its proof read as follows:

View attachment 9155In the third paragraph of the above proof by Stromberg we read the following:

" ... ... But , and so is an upper bound for ... ... " My question is as follows:

Can someone please demonstrate rigorously how/why ...

is an upper bound for ...
Help will be appreciated ...

Peter
 

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  • #2
Hi Peter,

By the definition of , for all However, and, by the choice for , Hence, contradicting the definition of .
 
  • #3
GJA said:
Hi Peter,

By the definition of , for all However, and, by the choice for , Hence, contradicting the definition of .
Thanks for your reply, GJA ...

It was most helpful ...

Peter
 
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