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A function \(g\) has the domain \(\mathbb{N}=\{1, 2, 3, ...\}\) and codomain \(\mathbb{N}\). The rule is "divide the input by 2".
  1. Write the function using formal notation.
  2. Explain why this rule does not define a valid function \(g: \mathbb{N} \to \mathbb{N}\).

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