That would let me derive your mother's phone number. https://xkcd.com/704/ https://xkcd.com/704/ It's different because there's nothing that says such a choice

That would let me derive your mother's phone number. https://xkcd.com/704/ https://xkcd.com/704/ It's different because there's nothing that says such a choice function _cannot_ exist (short of an axiom that says explicitly so).