**True or false**:

Let \( f: \mathbb N \rightarrow \mathbb N \) be a function such that \(f(n+1)>f(f(n)) \) for all natural numbers. Define \(g: \mathbb N \rightarrow \mathbb N\) as \(g(n)=f(n)-n\). Then, \(g \) need not be well defined.

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