If there are an infinite number of points between the trains when they are at the minimum distance, then there are also an infinite number of points between them when they are at 1 meter. So the trains would stay at one meter apart forever using that logic. In fact nothing would ever move anywhere. One thing that is not being considered is that these "halving" of distances are exponential, which leads to the paradox at infinity. The time factor would have to be exponential as well. With 2 exponential systems like that, the exponents could be removed to leave a linear based system. This would indicate that you would deal with addition for the 2 variables instead of multiplication, which is what the halving mehod uses. The use of addition will easlily allow the distance value of 0 to be reached.

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