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Yes, the problem was defined in such a way that there was an infinity problem. If I read your question properly, I translate it as:let d be a finite distance and v be a finite, non-zero velocity,d/v = ∞solve for v.The is no non-zero value that v can have to satisfy the equation. Infinity should usually be dealt with as a limit anyway...Now there are a few tricky ways out of your proposed problem:For instance, you can leave point A at any finite velocity headed away from point B, and never get there.
Consider your response "For instance, you can leave point A at any finite velocity headed away from point B, and never get there." is this the correct view of infinity. That you can't even head in its direction let alone get there.
OK lets restate the initial problem without the set velocity but make the distance between the points 1 Planck length with the time for the journey still infinite. How do we proceed?
No. You have already assumed a definition of infinity by "put the constraint on the system that it has to take an infinite amount of time...." and then abandoned it by making AB finite and d/dt (AB) finite. In other words, your question is self-inconsistent.
There is another solution that works if the distance between A & B is of a cosmological scale.If you set off from A at a finite velocity >0, the (accelerating) expansion of the universe will make it take an infinite time to reach B (ie it will never reach B in the lifetime of the universe).This solution does not involve any problems with infinities.
In other words, your question is self-inconsistent.
If you set off from A at a finite velocity >0, the (accelerating) expansion of the universe will make it take an infinite time to reach B (ie it will never reach B in the lifetime of the universe).
If we choose a finite distance from a point A to a spatially different point B that we wish to move an object and then put the constraint on the system that it has to take an infinite amount of time to move from point A to point B at a constant velocity then we can never find a solution that will work. We could argue that the interval of time could be infinitely short. However we do not want to violate the laws of physics in order to solve the problem. In this situation it looks like the object can never move from point A at all because any initial velocity would be finite and so could not take an infinite amount of time.
Well I was trying to make a point very badly which is my forte it seems.
Why go for the infinitely small singularity when we may go for the infinitely large universe? Could it be that we do the same mistake we have done before. We adapt the heliocentric point of view. When we look out in space we define physics in universe relatively our own limited world. The coordinates we use as common ground are those of our own backyard. It gets very complex with all systems we define in universe with our own backyard in the middle. Mathematics fail and we end up with a singularity. Perhaps this initial singularity somehow makes us infinitely big anyway?