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I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition).

I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...

I need help with the proof of Proposition 2.2.39 (b)

Proposition 2.2.39 (plus definitions of upper limit and lower limit ... ) reads as follows:

View attachment 9244

Can someone please demonstrate a formal and rigorous proof of Part (b) of Proposition 2.2.39 ...

Help will be appreciated ... ...

Peter

I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...

I need help with the proof of Proposition 2.2.39 (b)

Proposition 2.2.39 (plus definitions of upper limit and lower limit ... ) reads as follows:

View attachment 9244

Can someone please demonstrate a formal and rigorous proof of Part (b) of Proposition 2.2.39 ...

Help will be appreciated ... ...

Peter