Deeper than primes

[punshhh]

Finally! Someone who understands what doron is babbling about. So, punshhh, I guess you can provide the bijection between a set and its power set then? I assume it's easy, since it makes perfect sense to you.

I'm not going to get into the maths as that has already been stated.

Do you remember the discussion about an unbounded universe and how the posters taking the materialist position claimed that the universe is unbounded but not infinite and I asked for an explanation and didn't get one which remained unbounded.

Well we have a similar situation here, when you try to apply an infinity which can be understood by the mind to physical reality, ie spacetime it doesn't compute.

Do you accept this?

 

[laca]

I'm not going to get into the maths as that has already been stated.

No, doron has spectacularly failed to show a bijection between a set and its power set. You stated that hist theory makes perfect sense to you. I was hoping you could explain.

Do you remember the discussion about an unbounded universe and how the posters taking the materialist position claimed that the universe is unbounded but not infinite and I asked for an explanation and didn't get one which remained unbounded.

As usual, you have absolutely no idea what you're talking about. Where does a sphere begin? Where does it end?

Well we have a similar situation here, when you try to apply an infinity which can be understood by the mind to physical reality, ie spacetime it doesn't compute.

Do you accept this?

No. The only thing I accept at this point is that you have no *********** idea of any of this.

 

[epix]

epix, please show me a pair of points with 0 gap between them, and I will agree with Traditional Mathematics about the claim that a line segment is completely covered by a collection of distinct 0-size objects (known as points).

1. The real line is not emmental cheese. How can I show you the first point and the second point you asked for when it's been proven that the set of real numbers is uncountable?

2. As if you didn't read the tale of the Koch fractal, inspired by Peano, made of line segments whose number grows unbound. The property of R is such that there is no point in it which doesn't exist, even though the implication of the set theory is clear: there are more such points than the size of the set of characters necessary to define such a point.

The traditional math says that there is no house/gap in the real line that a point wouldn't be able to move in, even though you cannot see the U-Haul truck being unloaded in most of the cases.

Just show me a line segment that cannot be further divided. In fact, any line segment is a hotel with finite number of rooms that can accommodate number of guest/points whose number never stops to increase. But not every guest checks in at the desk -- you don't know the name, so you can't ask the receptionist to look up any guest.
http://www.tripadvisor.com/Hotel_Re...iews-Camino_Real_Motel-San_Antonio_Texas.html

As I said before, members of R are not adjacent to each other, like the guys in N, for example. If it was so, then R would be countably infinite set.

Your notion of the gap between real numbers is that some members of set R must be missing coz there are gaps in there. Wrong.

 

[punshhh]

No, doron has spectacularly failed to show a bijection between a set and its power set. You stated that hist theory makes perfect sense to you. I was hoping you could explain.



As usual, you have absolutely no idea what you're talking about. Where does a sphere begin? Where does it end?



No. The only thing I accept at this point is that you have no *********** idea of any of this.

The surface area of a sphere is a measurable size, so even though there appear to be no boundaries when walking on the sphere, sooner or later you find yourself walking over ground you've already covered. After a while you are unable to walk anywhere which you have not already covered. You have reached the point of no new ground in an apparently unbounded surface.
The sphere itself is the boundary.
Unless you can demonstrate a geometry with an infinite surface area, all dimensional states are bound in the same way.

It is only when you have an infinite quantity of spheres that you have in some sense an unbounded surface area spread over all the spheres.

This is fine but it requires an infinite spacetime, which has some unavoidable consequences, which the unbounded theory was devised to avoid.

 

[laca]

The surface area of a sphere is a measurable size, so even though there appear to be no boundaries when walking on the sphere, sooner or later you find yourself walking over ground you've already covered. After a while you are unable to walk anywhere which you have not already covered. You have reached the point of no new ground in an apparently unbounded surface.
The sphere itself is the boundary.
Unless you can demonstrate a geometry with an infinite surface area, all dimensional states are bound in the same way.

It is only when you have an infinite quantity of spheres that you have in some sense an unbounded surface area spread over all the spheres.

This is fine but it requires an infinite spacetime, which has some unavoidable consequences, which the unbounded theory was devised to avoid.

Instead of talking nonsense, how about showing a bijection between a set and its power set. After all, it makes perfect sense to you. Have you changed your mind?

 

[The Man]

The Man, the collection of all sub line segments that exist between the opposite edges of any arbitrary line segment, which follow each other by 0 gaps between them, cover that line segment if the opposite sub line segments of that collection have common edges with the considered line segment.

"opposite edges"? Do you mean the end points of that segment?

In the case of finite amount of sub line segments, one of the sub line segments can be the smallest one.

In the case of infinite amount of sub line segments, on one of the sub line segments can be the smallest one (we have ever smaller sub line segments).

In either case a line segment still has end points even if you just like to call them "edges". Which really is a misnomer as a line can be the edge of a plain or a plain the edge of a box (but we have been over that before).

We are not talking about a collection of sub line segments, where each one of them > point, whether there is finite or infinite amount of them along the considered line segment.

I was though, when you specifically and probably deliberately ignored it even after quoting it.

We are explicitly talking about the collection of points along the considered line segment, and this collection does not completely cover the considered line segment, whether the smallest sub line segment exists along the considered line (and in this case it is a finite collection of sub line segments along the considered line segment, which completely covers it) or only an ever smaller sub line segment exists along the considered line (and in this case it is an infinite collection of sub line segments along the considered line segment, which completely covers it).

Again we have been over this many times before in the set of real numbers the proper subset of points for the interval [1,5) does not include the point designated as "5". Nor does the proper subset set of points for the interval (5,10]. As such the union of those two subsets "does not completely cover the considered line segment" for the interval [1,10]. Just as the union of [1,4) and (5,10] doesn't. Where the latter union lacks a line segment as well as point "5" while the former union only lacked that single point. However, the union of [1,5) and [5,10] does "completely cover" [1,10]. You still seem to have problems understanding boundaries and how they may or may not be included in some set or subset.

In other words The Man, you still do not get the simple fact about the collection of infinitely many points (and not lines, whatever their size is, where all lines > 0) that can't completely cover any arbitrary given line segment.

In the same words used time and time again on this thread, two points define a line segment. In order to completely cover a line segment (in a non-discreet or continuous space) with other line sub-segments, such that there is no smallest line segment amongst them, then that line segment is de-facto completely covered by points. As in the example above with just the exclusion of one point of "the considered line segment" ([1,10] in the reals) from the sub-line segments means that no amount of sub-line segments can completely cover that "considered line segment". This is the same point about points, lines, line segments and continuous spaces, that has been made may times before that you still seem to be deliberately ignoring.

 

[epix]

Unless you can demonstrate a geometry with an infinite surface area, all dimensional states are bound in the same way.

Just bring an infinitely large piece of paper, if the demonstration you've asked for involves graphics. Meanwhile . . .

S = 4*pi*r² where r → ∞

That should do for the infinite surface area.

 

[punshhh]

Just bring an infinitely large piece of paper, if the demonstration you've asked for involves graphics. Meanwhile . . .

S = 4*pi*r² where r → ∞

That should do for the infinite surface area.

Now explain how this geometry relates to something which exists.

 

[punshhh]

Hi punshhh,

Please read http://www.internationalskeptics.com/forums/showpost.php?p=7034631&postcount=14798 .

As I see it your pointing out a paradox which occurs when applying infinities to dimensional space.

Is this how you see it?

 

[doronshadmi]

The real line is not emmental cheese.

epix, a one dimensional element exists independently of the zero dimensional elements that exist along it.

In other words, the zero dimensional elements that exist along a one dimensional element are only distinct zero marks along it, such that nothing is broken or divided.

epix, your weak reasoning still gets the real line only in terms of collection, without the simple understanding that a collection is an intermediate result between two building-blocks, which is at least an undivided one dimensional element and one or more zero dimensional elements that are used as marks along it.

How can I show you the first point and the second point you asked for when it's been proven that the set of real numbers is uncountable?

All the zero dimensional elements (where each one of them if a building-block and therefore an undivided object) that are used as marks along a one dimensional element, do not divide it simply because the a one dimensional element is exactly what it is (an elementary building-block).

As for the unaccountability of the real numbers, this is a mambo jambo fantasy reasoning, because I explicitly provide a systematic construction method of the all distinct members of infinite P(S) set, which explicitly demonstrate a bijection between all the members of the infinite S set and all the members of the infinite P(S) set.

epix, your weak reasoning can't understand the following:

http://www.internationalskeptics.com/forums/showpost.php?p=6996924&postcount=14618

http://www.internationalskeptics.com/forums/showpost.php?p=6986611&postcount=14585

and as long as this weak reasoning is your used reasoning, the best you can get is its mambo jambo fantasy.

Just show me a line segment that cannot be further divided.

Just show me a line segment (a one dimensional element) that is reducible into a set of distinct zero dimensional elements.

 

[doronshadmi]

Again we have been over this many times before ...

Time is not involved here in terms of before\after process.

Your serial-only reasoning can't comprehend the parallel aspect of present continuous state of infinitely many distinct zero dimensional building-blocks that can't completely cover a one dimensional building-block.

the union of [1,5) and [5,10] does "completely cover" [1,10].

Wrong, no amount of zero dimensional elements completely covers a one dimensional element.

In the same words used time and time again on this thread,

Again your serial-only reasoning rising its limited head.

two points define a line segment.

No, two points only mark two zero dimensional locations along a line segment. Given any infinite amount of zero dimensional locations along a line segment, it does not completely cover the considered line segment (there is always an uncovered one dimensional element between any arbitrary closer zero dimensional marks, along the considered one dimensional (known as line) segment).

In order to completely cover a line segment (in a non-discreet or continuous space) with other line sub-segments, such that there is no smallest line segment amongst them, then that line segment is de-facto completely covered by points.

Wrong reasoning. In the case of infinity sub-line segments, the smallest sub-line segment does not exist exactly because no line segment (a one dimensional building-block) is reducible into a point (a zero dimensional building-block).

As in the example above with just the exclusion of one point of "the considered line segment" ([1,10] in the reals) from the sub-line segments means that no amount of sub-line segments can completely cover that "considered line segment".

We are explicitly NOT talking about a line segment, which is indeed completely covered by sub-line segments ( as clearly and simply shown in http://www.internationalskeptics.com/forums/showpost.php?p=7030466&postcount=14789 , and you, The Man, can't comprehend it ).

We are explicitly talking about a line segment that is NOT completely covered by any given amount of points.

This is the same point about points, lines, line segments and continuous spaces, that has been made may times before that you still seem to be deliberately ignoring.

Please show me a zero dimensional line, or a one dimensional point, and I'll agree with you.

Once again, The Man, there is no before\after here but only present continuous, which is a state that your serial-only reasoning can't comprehend.

 

[doronshadmi]

As I see it your pointing out a paradox which occurs when applying infinities to dimensional space.

Is this how you see it?

There is no paradox.

No amount of 0-size elements completely covers a 1-size element.

 

[laca]

Instead of talking nonsense, how about showing a bijection between a set and its power set. After all, it makes perfect sense to you. Have you changed your mind?

I see you are avoiding the issue, punshhh. Why?

 

[epix]

Now explain how this geometry relates to something which exists.

Geometry isn't constrained by things that exist. You asked for a demonstration

Unless you can demonstrate a geometry with an infinite surface area, all dimensional states are bound in the same way.

so you got it. There was no stipulation that the object had to have finite dimensions.

I wonder what you been referring to by walking on the surface of a sphere. Doron is into 0-dim objects called points. Now show me something that exists but cannot be measured, as opposed to a sphere whose radius is finite.

 

[epix]

There is no paradox.

No amount of 0-size elements completely covers a 1-size element.

How much paint is needed to cover the surface of the earth? Finite amount or infinite? How much time is needed to peer into the crystal ball painted over pink to see the moment in the future where you would make sense?

 

[epix]

As for the unaccountability of the real numbers, this is a mambo jambo fantasy reasoning, because I explicitly provide a systematic construction method of the all distinct members of infinite P(S) set, which explicitly demonstrate a bijection between all the members of the infinite S set and all the members of the infinite P(S) set.

Why don't you do systematic mapping between the null set and its power set?

You think that 'a<--->b' means bijection, but that's not always so.

Proofs are not made of any constructions; they are made mostly of contradictory result of solved equations. For example, if a line cannot be "completely covered by points," then there are "gaps" in it and so point P bouncing randomly off the sides of square ABCD can escape from the square. How much time T is necessary for P to breach the perimeter of the square when the point hits any line of the square N times a second?

Set up the equations and when the result T turns out to be a finite number, then a line really cannot be "completely covered by points." Do some real math, instead of that incessant musing of yours.

 

[doronshadmi]

Do some real math, instead of that incessant musing of yours.

Indeed do some real math, instead of using your mambo jambo reasoning.

 

[doronshadmi]

Why don't you do systematic mapping between the null set and its power set?

Why can't you get http://www.internationalskeptics.com/forums/showpost.php?p=7030592&postcount=14791 ?

 

[doronshadmi]

How much paint is needed to cover the surface of the earth? Finite amount or infinite? How much time is needed to peer into the crystal ball painted over pink to see the moment in the future where you would make sense?

Infinite time if only 0-dimensional elements are considered.

 

[jsfisher]

Why can't you get http://www.internationalskeptics.com/forums/showpost.php?p=7030592&postcount=14791 ?

We all, except you, understand the post perfectly well. It contains no bijection between the null set and its power set.