# Example:Empty domain function

($1)$2 | $3 ($4) | $5 ($6)

For any set , there is exactly one function . It does not need a definition, because it is impossible to give it any input.

is vacuously well-defined: the definition is that for all , there is an value . This statement is vacuously true.

The uniqueness of is also vacuously true; to see this, expand the definition of uniqueness, and the definition of equality of functions.