To verify whether a function is one-to-one (or injective), we need to confirm that distinct inputs lead to distinct outputs. Specifically, for a function $f: \mathbb{Z} \to \mathbb{N}$, this means that if $f(a) = f(b)$, then it must follow that $a = b$.

Could you please provide the definition of the function $f$ so I can verify if it is injective?

Do you want details or have any questions?

Here are 5 relative questions that expand the topic:

1. How do you define the set of natural numbers for this function? Does it include zero?
2. What are the key properties of injective functions?
3. How would you prove a function is not one-to-one?
4. Can you give an example of a non-injective function?
5. How does surjectivity differ from injectivity?

Tip: To prove a function is injective, you can use a direct proof by showing that $f(a) = f(b)$ implies $a = b$, or use a contrapositive approach.