Actual Infinity in Reality?

[RoadRunner79]

[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

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.

So, how does that effect the logic I presented?
I don't see where saying that there is an upper bound of 1 is of any consequence, if the problem lies in reaching 1.   Again, this doesn't effect the logical issue;  it obfuscates it.

I notice that you keep using the words "assume" and "intuition"  whenever you talk about the case I'm making.  This despite the fact, that you ignore where I have shown that it logically follows to be the case.  On the other hand, you seem to just mostly insist that it is infinite, even though the method you used to demonstrate it as infinite also leads to a contradiction, when you also say it can be completed by sequentially following the points (also note, that this follows definitionally as well).  

It doesn't surprise me, that you have a group that gives this kudo's.   It doesn't surprise me, if talking about upper level math may wow some, that they don't really think about the issue.  There is one of two, who is giving you kudo's, who not that long ago, was dismissing me, as just an apologetic (when I was agreeing with them).   I'm an engineer, whenever possible, I think it is best to keep things simple, before looking at a more complicated solution.  I'm also cautious, when I ask a question, and the salesman starts going on with a bunch of technical sounding babble, that talks about any number of things, but doesn't address my question.