Lemma 2.2.10. Let \(a\) be a positive number. Then there exists exactly one natural number \(b\) such that \(b\pp=a\).
\(Proof\). See Exercise 2.2.2.
Lemma 2.2.10
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Exercise 2.2.3 (Propostion 2.2.12)
\(\equiv\) { Lemma 2.2.10: For a positive number \(n\), \(\exists! m,~ m\pp=n\) }
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Exercise 2.2.2 (Lemma 2.2.10)
Prove Lemma 2.2.10. (Hint: use induction. the induction here is somewhat degenerate, in that the induction hypothesis is not actually used, but this does not prevent the argument from remaining valid; cf. the discussion on implication and causality in Appendix A.2.)
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Chapter2
Exercise 2.2.2. Prove Lemma 2.2.10.