# Can a single point be considered a function?

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?

• I just want to tweak your terminology a bit. A set can include a single element. A single ordered pair can be considered a function. This includes the ordered pair $(1, 0)$, which maps the element $1$ to the element $0$. – Robert Shore Aug 31 '20 at 18:06

## 2 Answers

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 $$0$$.

• Thank you for the answer! Since ∅ is a function, that means it's a relation as well, correct? Or does a relation have to be between multiple sets? – n.n.n Aug 31 '20 at 18:14
• @NiehlsIngram Yes, the empty function is also the empty relation. – spaceisdarkgreen Aug 31 '20 at 18:15
• Great, thank you for the help! – n.n.n Aug 31 '20 at 18:17

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.