Can a single point be considered a function?

Question

A relation is defined as a set of ordered pairs. A set can include a single point. A function is a relation. Does that mean a single point can be considered a function? Say you have the point (1,0). There is a unique output for the input, but does there need to be multiple inputs and multiple outputs?

Answer 1

Yes, $\{(1,0)\}$ is a function. For that matter, $\emptyset$ is a function. A function can have a domain of any size, including $1$ and $0$.

Answer 2

In my view, any point can be considered function. Specifically, any function with a single answer and a single element may be a function. For example, {{1},{0}} can be Considered a function if the answer for f{1}~ {0} and the set contains the single element. Thank you for the cooperation. A function can also have a single element.