

If we adopt criteria of identity based of same location, next-moment-of-me will be not me, as I move, Earth move etc. It results in situation where I will die every millisecond.
We could also imagine situation where Omega put my copy in my location, but instantly moves me to the next room.
Clearly we can differentiate between different-location-same-time and different-location-different-time. Two things in different-location-same-time are different things. Two things different-location-different-time may be same thing or may be different thing depending on the path through time. Your mathematical style of abstraction in thinking about identity will only be useful at explaining the real world if it is matched to real world processes, and does not ignore important real world insights.