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I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some further help in fully understanding the proof of Proposition 8.7 ...Proposition 8.7 and its proof reads as follows:
View attachment 9397
View attachment 9398In the above proof by Browder we read the following:"... ... it follows from Proposition 8.6 that for some . In particular, taking above, we find for every , and hence ... ...
... ... ... "
My question is as follows:Can someone please explain exactly why/how that for every ... implies that ... ... ?In other words if some relation is true for every term of a sequence ... why then is it true for the limit of a sequence ... ...
Help will be much appreciated ...
Peter
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some further help in fully understanding the proof of Proposition 8.7 ...Proposition 8.7 and its proof reads as follows:
View attachment 9397
View attachment 9398In the above proof by Browder we read the following:"... ... it follows from Proposition 8.6 that
... ... ... "
My question is as follows:Can someone please explain exactly why/how that
Help will be much appreciated ...
Peter
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