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Assuming An Infinite Number Of Points...

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Posted by Rntt... on September 18, 1998 13:52:24 UTC

: Everyone, thanks for your help : I have one further question. My original question was how could two trains collide seeing that there are an infinite amount of points between the two trains. I would think the trains would continue to travel along this string of infinite points never reaching its destination ( the collision). But here is another way to look at it. As the trains came closer and closer towards each other, the amount of space remaining between the trains would shrink. Now if we were to magnify this remaining space, and zoom in at the same rate the space is shrinking, we could maintain a view of this empty space. So... how would this empty space ever disappear, Or how would this empty space ever close and allow the trains to touch?

I still haven't been completely won over to this digitised space idea, but let me put to you this question.

If there are an infinite number of points, then these points are infinitely small, do you agree? So, the trains would pass an infinite number of points per any unit of time.

Therefore, your camera would have to be zooming at an infinite rate.

Now, your question makes a few assumptions about the nature of infinity. First of all, what happens when you divide infinity by infinity? This calculation would be required to answer your question. Since infinity is a theoretical concept, rather than a number, then it is impossible to say. It most likely doesn't obey the same laws as mathematics.

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