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?

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    $\begingroup$ 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 $0$. $\endgroup$ – Robert Shore Aug 31 '20 at 18:06

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 $0$.

  • $\begingroup$ 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? $\endgroup$ – n.n.n Aug 31 '20 at 18:14
  • $\begingroup$ @NiehlsIngram Yes, the empty function is also the empty relation. $\endgroup$ – spaceisdarkgreen Aug 31 '20 at 18:15
  • $\begingroup$ Great, thank you for the help! $\endgroup$ – 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.


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