Item 3.

\(h:\{1,2,3,4\} \to \N\) defined by the table:

Here the domain is the finite set \(\{1,2,3,4\}\) and to codomain is the set of natural numbers, \(\N\text{.}\) At first you might think this function is the same as \(f\) defined above. It is absolutely not. Even though the rule is the same, the domain and codomain are different, so these are two different functions.