Example:Empty domain function

From CS2800 wiki

For any set [math]A [/math], there is exactly one function [math]f : \href{/cs2800/wiki/index.php/%E2%88%85}{∅} \href{/cs2800/wiki/index.php/%E2%86%92}{→} A [/math]. It does not need a definition, because it is impossible to give it any input.

[math]f [/math] is vacuously well-defined: the definition is that for all [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} \href{/cs2800/wiki/index.php?title=%5Cemptyset&action=edit&redlink=1}{\emptyset} [/math], there is an value [math]f(x) \in A [/math]. This statement is vacuously true.

The uniqueness of [math]f [/math] is also vacuously true; to see this, expand the definition of uniqueness, and the definition of equality of functions.