Actual Infinity in Reality?

[polymath257]

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


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.

You reach x=1 when t=5. Simple enough. You reach each and every one of those points also. There is no contradiction here.

Yes, for each one of those points, there are infinitely many you still have to go through to get to 1.

Yes, you do go through all those points.

Yes, you also go through 1.

No, you did NOT show it follows logically that you cannot get through every point. You are making assumptions that it is impossible to go through an infinite number of points. THAT is your mistake. And no, you did NOT show a contradiction: we have an infinite set that is also bounded. Your problem is a mix of different notions of 'bounded' or having an 'end'. The fact that there are two distinct concepts here is part of your confusion.

I'm sorry, but it is *you* that isn't thinking about the issue. In the scenario we have been discussing, you *do* go through every point of the sequence **and* you reach 1. There is no contradiction there *unless* you assume that it is impossible to go through an infinite number of points.

Your question has been addressed multiple times. Evidently you have refused to learn enough to understand the answer.

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Just a heads up: I'm going to be going on vacation starting on Friday and won't be able to post for about 10 days. Don't expect any answers from 3/9 through 3/19.