Is the set of ordered pairs $\left\{(1,2),(2,3),(1,4)\right\}\}$ a function? Choose the correct statement.

It is not a function because the outputs are not strictly increasing, and $2$ and $4$ are different

It is not a function because the input $x=1$ corresponds to two different outputs ($2$ and $4$)

It is a function because there are exactly three ordered pairs listed, and having three pairs always makes a relation a function

It is a function because each ordered pair is unique, even if inputs repeat, and the uniqueness of the pairs guarantees its status as a function