Actual Infinity in Reality?

[polymath257]

The two statements in bold are false. The failure of the first bold statement invalidates the second. The rest of the statements are all correct.

And, in fact, if you look at my description, you see why the bold statements are false.

Remember, to go through all those points means that there is a time corresponding to each point. And that is true.

So, yes, if you have not reached the end, there is always another point to go through (in fact, an infinite number of points to go through) and you do reach the end.

Your assumption that we cannot go through an infinite number of points is invalidated.

Those statements follow logically from those that proceeded it.
Here they are again

If there is always another point, that is not the end, and which precedes the end, then end cannot be reached.
Therefore the end position is not reachable if there is an infinite number of points which must be traveled. 
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If all points prior to the destination must be passed through sequentially, before reaching the destination; and there is an infinite number of points prior to destination so that the next point is always not the destination.  Then the end position will not be reachable.

It cannot be without end, and end at the same time... this is the contradiction.   Now perhaps you assume that your model is infinite, and you can calculate any infinitely small point and corresponding time.  However, this is why I asked numerous times previously, what exactly your points represent, in a real world motion.  If your model is only conceptual, then I suppose you can have whatever you want.   You don't actually traverse an infinite number of points in your model, you just assume that you do.  And if you actually follow the same math that shows that it is infinite, it also shows you that it cannot be completed.    Your model appears to be logically incoherent.

And, again, it is two different notions of 'having an end'. If the difference is kept in mind, the issue resolves itself.

1. In the sequence: whenever you are in the sequence, there is another term of the sequence later on. In this sense, the sequence does not end. But this is irrelevant to whether you go through every point.

2. In the interval between 0 and 1: In this sense, the sequence has an 'end'. More technically, it has an upper bound. And 1 is an upper bound. This is the sense that is important in asking if we go through every point. Since each point corresponds to a time, we do, in fact, finish that sequence.

The point here is that the sequence has an upper bound, but that upper bound is not in the sequence. There is no contradiction here, just an opportunity to learn.

My points represent locations between the two points. Again, what does it mean to 'traverse an infinite number of points'? It *means* that for each point, there is a time when we are at that point. And that is the case here. So, yes, we do traverse an infinite number of points. You intuition that this is impossible is just wrong.

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[quote='polymath257' pid='1711158' dateline='1520172357']

The two statements in bold are false. The failure of the first bold statement invalidates the second. The rest of the statements are all correct.

And, in fact, if you look at my description, you see why the bold statements are false.

Remember, to go through all those points means that there is a time corresponding to each point. And that is true.

So, yes, if you have not reached the end, there is always another point to go through (in fact, an infinite number of points to go through) and you do reach the end.

Your assumption that we cannot go through an infinite number of points is invalidated.

Those statements follow logically from those that proceeded it.
Here they are again

No, you added another assumption: that you cannot go through an infinite sequence of points. That assumption is wrong, and I showed how it is possible.

Here are two situations:

1. At time t=1, we go through the first point. At time t=2, we go through the second point. At time t=3, we go through the third point, we continue and go through the n^th point at t=n.

If *this* is your scenario, then we will never get through all of the points.

2. At t=2.5, we go through the first point (located at x=.5), at t=3.75, we go through the second point (located at x=.75), at t=4.375, we go through the third point (located at x=.875). We continue, and go through the point located at x at time t=5*x.

In *this* scenario, we get through all of the points and we get to x=1 when t=5.

As far as I can tell, you are imagining the first scenario. But the second scenario is how it actually happens.

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If you are discussing motion, then time is a factor.

Sure, so are accelerations and deceleration, and if your dealing with actual motion, then it's likely not going to be perfectly consistent all the way through.

However what I was saying didn't involve time, and I don't see where adding time in, effects it.  So while it is assumed that there is motion, that one is traversing the path of the line in some manner; the amount of time, or the even constant motion is not a factor.

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Time is a factor because to 'go through a point' means that there is a time when you are at that point. So the timing is everything. The constant speed simplifies things so we can say *exactly* when we go through any particular point.
Once again, for each point in that sequence, there is a time when we are at that point. AND there is a time when we are past every term in that sequence.
The sequence is bounded above, but that bound is not in the sequence. That seems to be your main issue. But that isn't a contradiction.