Empty function, what is it?

I meet with term 'empty function' from time to time. It's high time to understand its nature. What is field( set of arguments) and what is image? ( set of value)?

• Do you know the definition of function? – Git Gud Oct 20 '14 at 16:20

The set theoretic definition of a function $f:A\rightarrow B$ is a special type of binary relation. I.e. it is a subset of $A \times B$. The empty set is also a subset of $A \times B$ and is defined as the empty function.
• Yeah, specifically the empty relation is a function iff $A$ is empty. – Seth Oct 20 '14 at 16:28