Actual Infinity in Reality?

[polymath257]

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.

Well we are just repeating ourselves anyway.... and you refuse to look at the logic.   I don't dispute that in a conceptual geometric model, that you have a theoretical point in time, for any infinitesimal point in distance.  However the question is, in something real, what does this "point" represent?   What are you saying is the actual infinite?  As well, when you actually follow the model you are presenting to show and actual infinite and do the math, at no point will you ever reach the end (which equates to the definition of infinite).    This is not an assumption, but a fact.  You can do that calculations by hand, you can make a computer model, neither will ever reach the end (which is why you use those methods to show an infinite to begin with).    You seem to be assuming an infinite, and assume that any "point" you can make up on paper, correlates to something in real motion, and then ignore the logical contradiction of your assumptions.  As an engineer, I would say you need to get out of the office (or classroom) a little more.

(edit to add)   Also as for bringing up modern physics theories and such, there is the notion of a Planck length.  Where it is theorized, that classical ideas concerning space time, break down, and quantum effects take over.   That at this point, any distinction between two points is indistinguishable.  You might also keep in mind, that things are always moving (vibrating back and forth)

Since we don't seem to be getting anywhere... I leave you to get ready for your vacation; I hope you have fun.

A point represents a location between 0 and 1. Wasn't that obvious?

And yes, there is an infinite number of such points.

And yes, we *do* reach the end. The *logic* that I presented shows that. Your *claim* is based on a faulty *assumption* that you cannot a complete an infinity. And no, that is NOT a fact. Remember, to be infinite *only* means that it cannot be put into correspondence with some counting number. it does NOT mean 'has no bound'. it does NOT mean 'goes on forever'. it does NOT mean 'has no end'. The example of the sequence we have been considering shows the differences.