Problems pending

chap 7 infinite inf problem
Chap 8 whole
(Ex. 8.1.1
Ex. 8.1.9
Ex 8.1.10)
Chap 9: heine-borel Theorem, f being convergent at xo equivalent statement problem
supremum definition for functions
exponentiation functions are continuous
9.5 question
Finbonacci sequence a
principle of strong induction (for fibonacci especiallly )
Example 9.8.4
Exercise 9.8.4
Exercise 9.8.5

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How to make best notes

My strategy would be: To rigorously prove everything that you would use in the future(e.g, reals have the sup inf property) Make a comments column where you put down why you did that step. In the last write the general strategy you used for the proof(e.g, in the sup inf case make the bound shorter for the last values) If you are doing a study of a particular field say Analytic Number Theory then make a content sheet of pdf format preferably so that you could find whatever proof you want to have a look on.It should be an exhaustive list.
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