Actual Infinity in Reality?

[RoadRunner79]

Back to the topic.... I think there is an question that wasn't answered, that should be.

  If it is said, that a line contains a continuum of points (however you choose to define them).  Despite the fact, that this supposed infinity ends at 1 which is contradictory to saying that it is infinite in number in itself. (note:  I'll use one as a destination in this writing, although it may be another length)   What is the point immediately prior to 1?  There is necessarily an instance, where you transition from "not 1" to "1" while traveling along this line. 

I don't think that those proposing an actual infinite can answer the question.   I believe that this question shows the bait and switch that is occurring (whether the presenter knows it or not).  I think it is also why I have found difficulty in these conversations in having someone define what the term "point" is.  (It much easier to play fast and loose, if you do not define your terms).  If the points along the line are in fact infinite, then there cannot be a transition from "not 1" to "1".  As the argument goes, no matter how small the number is between our last point and the destination, we can always make up another number which is yet smaller (nature of the decimal system).  And we can repeat this over and over again, never reaching 1.  The time doesn't matter; this will never end (which is correctly  the definition of infinite) .   This is what Zeno's dichotomy (runners) paradox shows .   And I don't think that this is being addressed.  To get from "not 1" to "1"  you have to end the infinity (thus not infinite).

If you follow the logic and the procedure that is used to get an infinity in this way, then you cannot logically reach the destination either (not if you are consistent).  Adding an infinity of points of time, does not change here that the process will never end (which is why time is inconsequential).  The fact, that it does end, and that motion is possible, shows that this idea of a infinity in any given line and any given motion, shows that this idea is not logical (or at least the way it is argued is not logical).  

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Why do you assume there is a point just before 1? In fact, I can prove that, in fact, there is no point that is the 'last point before 1'.

The proof is a simple one done via proof by contradiction. Suppose x is any point before 1, so x<1. Let y be the average of x and 1. Then x<y<1, showing x is NOT the last point. hence, no last point can exist.

We cannot 'reach the destination' IN THAT WAY. We still reach the destination, but not via stopping at each of those infinitely many points.

I'm not saying that you have to stop at the point. Passing  through is fine.  

Your demonstration did not offer a rebuttal, but further re-enforces my point.  This is exactly what I was saying. 

It's your own point that you are saying there is a contradiction with, even though you keep saying that there is no contradictions.  This is why myself and Steve are saying that you will never reach the destination of 1. 

This is using the same reasoning that you used to say that there is an infinite number of points, and showing that by that reasoning you cannot reach the destination.


Now if you would want to get into what you are calling an assumption that there is a point prior to our destination (A) where it is (!A); we can work through that.  However any way you get around this, I believe is going to cause you to abandon your model which is giving you an infinite number of "points".