(February 13, 2018 at 5:16 pm)RoadRunner79 Wrote: 1.)   It is unbound by definition, you can't have it complete and thus bound.  An actual infinity keeps going and going with more to go after that.  It doesn't finish, hence an infinity

Let me just focus on this one for now, because I feel like this is your biggest hurdle.

Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.


About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have, IF motion were to be defined classically and A-theory of time assumed? In the abstract world of mathematics, everything is static and lines are abstractly perfect even if, in the real world, they are not drawn perfectly. But in this universe at least, it does seem like Zeno's paradox may be pointing to a quantized universe in terms of space divisibility and in terms of time (so discrete rather than continuous)?

(February 13, 2018 at 7:47 pm)Grandizer Wrote:

(February 13, 2018 at 5:16 pm)RoadRunner79 Wrote: 1.)   It is unbound by definition, you can't have it complete and thus bound.  An actual infinity keeps going and going with more to go after that.  It doesn't finish, hence an infinity

Let me just focus on this one for now, because I feel like this is your biggest hurdle.

Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.

How do you complete an infinity?  It seems you cannot by definition to me.

(February 13, 2018 at 7:50 pm)RoadRunner79 Wrote:

(February 13, 2018 at 7:47 pm)Grandizer Wrote: Let me just focus on this one for now, because I feel like this is your biggest hurdle.

Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.

How do you complete an infinity?  It seems you cannot by definition to me.

I don't have to complete anything. That's the thing. It's already complete but boundless.

(February 13, 2018 at 7:51 pm)Grandizer Wrote:

(February 13, 2018 at 7:50 pm)RoadRunner79 Wrote: How do you complete an infinity?  It seems you cannot by definition to me.

I don't have to complete anything. That's the thing. It's already complete but boundless.

Can you add one more?  How about subtract one more?    If so, then how is it complete?

Edit:   Or what do you mean by complete?

(February 13, 2018 at 7:47 pm)Grandizer Wrote:

(February 13, 2018 at 5:16 pm)RoadRunner79 Wrote: 1.)   It is unbound by definition, you can't have it complete and thus bound.  An actual infinity keeps going and going with more to go after that.  It doesn't finish, hence an infinity

Let me just focus on this one for now, because I feel like this is your biggest hurdle.

Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.


About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have, IF motion were to be defined classically and A-theory of time assumed? In the abstract world of mathematics, everything is static and lines are abstractly perfect even if, in the real world, they are not drawn perfectly. But in this universe at least, it does seem like Zeno's paradox may be pointing to a quantized universe in terms of space divisibility and in terms of time (so discrete rather than continuous)?

Of course comparing the existence to a hotel is just silly

(February 13, 2018 at 7:58 pm)RoadRunner79 Wrote:

(February 13, 2018 at 7:51 pm)Grandizer Wrote: I don't have to complete anything. That's the thing. It's already complete but boundless.

Can you add one more?  How about subtract one more?    If so, then how is it complete?

Edit:   Or what do you mean by complete?

Forget the hotel example.

Let's do set theory. Complete as in every possible element of an infinite set of integers (infinite both ways) is already there. How can you add more new elements to the set when it's complete?

You can simultaneously add +1 to each of the elements, sure, and each of the elements will then increase by 1, but it would still be the same infinite size because it's complete (I think, correct me if wrong, guys).

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(February 13, 2018 at 7:59 pm)Tizheruk Wrote:

(February 13, 2018 at 7:47 pm)Grandizer Wrote: Let me just focus on this one for now, because I feel like this is your biggest hurdle.

Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.


About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have, IF motion were to be defined classically and A-theory of time assumed? In the abstract world of mathematics, everything is static and lines are abstractly perfect even if, in the real world, they are not drawn perfectly. But in this universe at least, it does seem like Zeno's paradox may be pointing to a quantized universe in terms of space divisibility and in terms of time (so discrete rather than continuous)?

Of course comparing the existence to a hotel is just silly

That's true. It's a nice hypothetical, regardless.

(February 13, 2018 at 7:47 pm)Grandizer Wrote: About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have

Math has it;s limits..but in this context that isn;t ne of them.

Consider the following;  I place you in a rubber room with a piece of granite.  You can't actually break it in half.but that doesn't mean it doesn't have two halves, hemispheres, if you will.  Further, your practical inability to break a piece of granite in two in a rubber room does't mean that each of those hemispheres can't be divided into quadrants.  So on and so forth.  Whereas once it was thought that an atom was indivisible, it was always similar to a piece of granite in this regard..and in truth we learned that we could split them practically as well.  Now we're down to the subatomic..and while at some point we have no practical ability to split x..this doesn't make the concept of the hemispheres and quadrants (ad infinitum) of x any less intelligible or valid.

(February 13, 2018 at 8:05 pm)Grandizer Wrote:

(February 13, 2018 at 7:58 pm)RoadRunner79 Wrote: Can you add one more?  How about subtract one more?    If so, then how is it complete?

Edit:   Or what do you mean by complete?

Forget the hotel example.

Let's do set theory. Complete as in every possible element of an infinite set of integers (infinite both ways) is already there. How can you add more new elements to the set when it's complete?

You can simultaneously add +1 to each of the elements, sure, and each of the elements will then increase by 1, but it would still be the same infinite size because it's complete (I think, correct me if wrong, guys).

You ask, how can more numbers be added if it is complete, but by definition an infinite amount is never completed. I think you are switching to sets now, because you can abstractly complete the set just add "..." . You loosely define it, to include any possible integer. You want to increase the set... you just loosen the definition. So you either end up with a contradiction (it is both complete and not complete at the same time in the same way). Or what you mean by complete is not the same. Or you mean infinite in another way.

(February 13, 2018 at 7:22 pm)RoadRunner79 Wrote:

(February 13, 2018 at 6:25 pm)polymath257 Wrote: Yes, an infinite number of finite numbers.

I gave the argument above for the collection being infinite. It is a simple argument. As long as you admit that there is a point between any two given ones (no matter what the definition), the result follows.

I think that there a couple of problems with this as a refutation.   I think that you point is an abstraction, which is why you do not want to define it.  I also think that if you do define it, as anything physical and finite, your argument fails.  It's also on this point, that you have an issue, because the contention is that you cannot have an infinite number of things by successful addition (or division or multiplication for that matter).   No one is arguing that you cannot have an infinite set of abstract numbers (which is really all I think your points are).  If you disagree, then give a definition which is not an abstract, and we can test it.  I think that your point is zero (or nothing), or always changing and not talking about the same thing.

Secondarily similar to successive addition, you will never reach an actual infinite by successive division.  At any given step in the process, you only have a potential infinite.  You don't posses and actual infinite at any time, but are extrapolating out the action infinitely.

Wrong again. Look at the entire collection of points. Because they are on a line, there have an order (directionality) to them. If there are only finitely many, say N, we can write them as
x_1 < x_2 <...x_N
(say, from left to right). Remember that this is assumed to be the *complete* list. That is the assumption of finiteness.

But then, there is some point y with x_1 <y<x_2. In other words, y is between those first two points. And so y is NOT in the list you started with. In other words, that list was NOT complete. That contradiction shows there cannot be a complete list of points that is finite. In other words, the complete list of points is infinite.

I'm not doing successive division. I am doing *one* division to show the assumed finite list cannot be complete.

And this isn't a 'potential infinity' (damn, I hate that phrase---very bad philosophy). The whole collection of points is there and completed. And I just showed that it cannot be a finite collection of points. So it must, by definition, be infinite.

You don't have to be able to do the subdivision an infinite number of times. You just need to be able to do it *once* to show that having a finite total number of points is contradictory.

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(February 13, 2018 at 7:58 pm)RoadRunner79 Wrote:

(February 13, 2018 at 7:51 pm)Grandizer Wrote: I don't have to complete anything. That's the thing. It's already complete but boundless.

Can you add one more?  How about subtract one more?    If so, then how is it complete?

Edit:   Or what do you mean by complete?

The complete collection of points on a line segment has every point on that line segment. No point can be added that is in that line segment. Yes, you can take a point away. You can take infinitely many points away. If you do the latter right, you will still have infinitely many points left over.

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(February 13, 2018 at 8:23 pm)Khemikal Wrote:

(February 13, 2018 at 7:47 pm)Grandizer Wrote: About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have

Math has it;s limits..but in this context that isn;t ne of them.

Consider the following;  I place you in a rubber room with a piece of granite.  You can't actually break it in half.but that doesn't mean it doesn't have two halves, hemispheres, if you will.  Further, your practical inability to break a piece of granite in two in a rubber room does't mean that each of those hemispheres can't be divided into quadrants.  So on and so forth.  Whereas once it was thought that an atom was indivisible, it was always similar to a piece of granite in this regard..and in truth we learned that we could split them practically as well.  Now we're down to the subatomic..and while at some point we have no practical ability to split x..this doesn't make the concept of the hemispheres and quadrants (ad infinitum) of x any less intelligible or valid.

But we can *still* talk about positions and half-way positions, etc. Even if the measured distances are quantized, the whole collection of real number are potential eigenvalues for the position operator.

Why do you say that a potential infinite is bad philosophy? Also still wondering what a point is? It apparently doesn’t relate to the length of the other two points. What do you do with these points?