In mathematics, assuming 'void' is the empty set, the function void -> a exists, but is kind of trivial because it never returns anything, however functions a -

In mathematics, assuming 'void' is the empty set, the function void -> a exists, but is kind of trivial because it never returns anything, however functions a -> void can't exist because they'd have to return an element of void, which don't exist, the one exception being the function void -> void. Denoting A -> B as B^A this translates to: a^0 = 1 0^a = 0 0^0 = 1 The fact that there's precisely 1 function void -> a is considered rather special in category theory, and means that 'void' is the so called 'initial object' for the category (which is automatically unique up to isomorphism).