I am reasonably sure that this won’t happen, or said another way, a function that returns the minimum delta between any finite pairs of lists is a reasonably we

I am reasonably sure that this won’t happen, or said another way, a function that returns the minimum delta between any finite pairs of lists is a reasonably well behaved function wrt the length of the list and the size of the integers and doesnt just zoom off to infinitely close to zero ever. Said yet another way, the ways in which real numbers are dense is spooky and almost totally untied to how rationals work, and i do not believe you can get there from here using square roots.