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- Jun 22, 2012

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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 help in fully understanding the proof of Proposition 8.7 ...

Proposition 8.7 and its proof reads as follows:

In the above proof by Browder we read the following:

"... ... Thus, \(\displaystyle \{ S_m \}\) is a Cauchy sequence in \(\displaystyle \mathscr{L} ( \mathbb{R}^n )\)... ...

My question is as follows:

Can someone please demonstrate formally and rigorously that \(\displaystyle \{ S_m \}\) is a Cauchy sequence in \(\displaystyle \mathscr{L} ( \mathbb{R}^n )\)... ...

Help will be much appreciated ...

Peter

===============================================================================

Note: Browder defines a Cauchy Sequence in a metric space as follows:

Hope that helps ...

Peter

I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...

I need some help in fully understanding the proof of Proposition 8.7 ...

Proposition 8.7 and its proof reads as follows:

In the above proof by Browder we read the following:

"... ... Thus, \(\displaystyle \{ S_m \}\) is a Cauchy sequence in \(\displaystyle \mathscr{L} ( \mathbb{R}^n )\)... ...

My question is as follows:

Can someone please demonstrate formally and rigorously that \(\displaystyle \{ S_m \}\) is a Cauchy sequence in \(\displaystyle \mathscr{L} ( \mathbb{R}^n )\)... ...

Help will be much appreciated ...

Peter

===============================================================================

Note: Browder defines a Cauchy Sequence in a metric space as follows:

Hope that helps ...

Peter

Last edited: