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Solutions to Understanding Analysis by Stephen Abbott (second edition)
In Exercise 1.3.10 (b), we are asked to show that the Cut Property implies Axiom of Completeness. In your answer, you first construct set A and B, and then show...
The term rewrite should be $a_n = \(1 + 1/2^{n-1})$, not $a_n = (1 + 1/n)$. Using the result from 2.4.10 implies the product converges since $\sum{(1/2^{n-1})}$ converges.
The solution to exercise 2.7.5 states that "Eventually we have $1/n^p 1$ (polynomial vs exponential) meaning we can use the comparison test to conclude [that the p-series with $p>1$ converges]....
2.4.7 (b) Changed liminf(a_n) from lim(z_n) to lim(x_n), for consistency and to line up with my changes to (d). (d) Original proof was not biconditional and lacked some details; added...
Thank you for your contribution, which really helps me alot. Yet, I found a minor error in ex 1.5.6 involving the argument in countability. > For any nonempty interval $I_n$...
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Solutions to Understanding Analysis by Stephen Abbott (second edition)