empty function

Given a set $X$, the **empty function** to $X$ is the function to $X$ from the empty set. This always exists and is unique; in other words, the empty set is an initial object in the category of sets.

The empty function to the empty set is *not* a constant function.

Last revised on July 27, 2013 at 19:45:59. See the history of this page for a list of all contributions to it.