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lines changed Original file line number Diff line number Diff line change 6464\begin {ex }
6565Multiplication is a function because it pairs each input---each pair
6666of natural numbers---with a single output: $ \times \colon \Nat ^2 \to
67- \Nat $ . By contrast, the square root operation applied to the domain
68- $ \Nat $ is not functional, since each positive integer $ n$ has two
69- square roots: $ \sqrt {n}$ and $ -\sqrt {n}$ . We can make it functional by
67+ \Nat $ . By contrast, mapping a natural number~ $ n $ to a real~ $ x $ such
68+ that $ x^ 2 = n $ is not functional, since each positive integer~ $ n$ has two
69+ square roots: $ \sqrt {n}$ and~ $ -\sqrt {n}$ . We can make it functional by
7070only returning the positive square root: $ \sqrt {\phantom {X}} \colon
7171\Nat \to \Real $ .
7272\end {ex }
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