While playing with my little sister earlier we where inventing distances form earth to sun/stars/planets and who had the bigger distance wins. Now at some point she said "from earth to jesus" and since i'm not sure about his existence i was wondering , what if jesus does not exist? Then this distance is the distance form a point on earth to the empty set. Now i was wondering if such a distance is geometrically defined. Is there for example a value or definition for the distance on the real line between a number and the empty set? In euclidian space? In general? I have no knowledge of topology..maybe i could find an answer there?
I hope this is not a silly question , but i want to know who wins (: