A spaceship sets off from Earth on an intergalactic exploration - blast off. Now imagine it's been travelling at 50,000 miles per second for 100 million years – it’s very far away by now, and the on-board computer has been recording the spaceship’s position whilst travelling through space.
All is well and good – the spaceship has been travelling continuously through unbroken space, i.e., the continuity of the spacetime continuum has so far remained intact, so there’s no problem yet!
According to the conceptual meaning of infinite straight-line distance, regions of space must already exist infinitely far away – i.e., actually already exist to potentially be occupied by physical stuff – potentially it has to be as valid for objects to already exist in these supposed regions, as it is for us to exist here on Earth.
Problems arise when trying to comprehend what it would take for our spaceship to arrive at such supposed infinitely faraway regions of space – it might seem silly, but our spaceship cannot possibly be any closer to such regions than it was before it started its journey here on Earth, even after having travelled such a vast distance in the vastness of space.
Consider where and how such infinitely faraway regions meet up with regions that our spaceship has so far managed to travel to? If there’s no break in continuity, there must be a meeting up point somewhere along the way for our spaceship from its perspective, and also from the perspective of anything situated at such an infinitely faraway region that could be travelling towards the spaceship, such as robots on an exploration.
Head-on collision: Imagine that our spaceship and the robots are now travelling towards each other, never getting any closer to each other – millions of more years travelling and still no closer whatsoever – what would it take for them to get closer?
Relative position error: What is the physical nature of the space that supposedly exists between our spaceship and the robots as they head towards each other – can we even sensibly say that they are headed towards each other when we consider they’re not actually closing the gap (don’t have relative positional coordinates to each other)? In reality this is a physical impossibility of course.
Conclusion: Obviously, the situation as described above is absurd! Yes, indeed it is, but any such robots needn’t worry about not being able to meet us here on Earth, because that isn’t our reality – there aren’t any infinitely faraway regions of space – space is finite.