# Functions

Algebra Level 3

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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