TITLE: Explain "There is a unique function from $\emptyset$ to any set $A$".
QUESTION [5 upvotes]: My book says:

There is a unique function from $\emptyset$ to any set $A$. 

I don't understand how that is. Let $A=\{1,2,3\}$. Which element of $A$ do we map $\emptyset$ to? Do we map $\emptyset$ to $\emptyset$? But $\emptyset\notin A$!
Thanks.

REPLY [3 votes]: Recall that a function from $X$ to $Y$ is a subset of $X\times Y$ which has some particular properties.
If $X=\varnothing$, what is $X\times Y$? and how many subsets does it have?