Thoughts on the scale of the universe?

[FallentoReason]

"Achilles and the tortoise are going to run a race. Achilles, being confident of victory, gives the tortoise a head start. Before Achilles can overtake the tortoise, he must first run to point A, where the tortoise started. But by then the tortoise has crawled to point B. Now Achilles must run to point B. But by then the tortoise has gone to point C, etc. Achilles is stuck in a situation in which he gets closer and closer to the tortoise, but never catches him."

I don't think that true. From memory I remember in highschool maths there was a vector question that had the same description mathematically as this. If you crunch some numbers, you'll find that Achilles catches up to the tortoise. It's common sense really, because the faster object will inevitably catch up to the slower object infront of it.

The thing is though, that this question words it in a tricky way. It's making you think about the situation at certain points in time, primarily, everytime Achilles gets to the point where the tortoise used to be after he last reached a similar point. Even through this reasoning though one can imagine that the distance between 'ghost tortoise' (Achilles' position that he reaches every time) and true tortoise is getting smaller everytime you pause and measure.

there couldn't possibly exist an infinite number of dissections on a line segment, being that it is of finite size (please correct me if I'm wrong).

You can keep slicing infinitely. Think of a line segment from 0 to 1. Chop that in half. Now we have 0 to 0.5. Chop that in half. Now we have 0 to 0.25.....now we have 0 to 0.000000000001. Chop that in half ad infinitum.

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In terms of the universe being infinitely large, I think the only requirement for that is that it can't be bounded, therefore by mathematical definition, infinite.