Deeper than primes

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zooterkin said:
Ah, yes, another of those words you have trouble with; that post does not clearly show anything except some lines joining some arbitrary points on the circles. How did you choose those particular points, and what about all the ones inbetween?

Also, there is no X in that post at all...
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X is the beginning AND an end point of each closed form.

All we have to do is to visit each point no more than twice (one visit is called beginning and the other visit is called end and it is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152).

In the case of an infinite collection the arbitrary beginning X point of a closed form is visited only once.
 
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We're waiting for you to provide a definition of one of the many terms you toss around here. I thought you were going to provide one for 'closed pointless curve', but nothing apart from some drawings so far.
 
zooterkin said:
We're waiting for you to provide a definition of one of the many terms you toss around here. I thought you were going to provide one for 'closed pointless curve', but nothing apart from some drawings so far.
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A pointless closed curve is a primitive.

If points are found on it, then we deal with a complex, and as I showed in http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 order has no significance when the points are visited (no more than twice) along the closed curve.
 
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doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 clearly shows that X is a beginning AND an end point only if the collection is finite.
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Nope, until you define what constitute a “beginning AND an end” you have no basis to claim that aspect is limited to only a finite collection.


doronshadmi said:
If the collection is infinite then X is a beginning-only point exactly because no Y is comparable with it (if it was true that Y is comparable with X, then X was both a beginning AND an and of the given infinite collection).
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Again simply you claiming that you can not make comparisons in an “infinite collection”. Simply a limitation of you and you notions, which also restrict you from comparing X and Y to determine which if any or both, is “a beginning-only point”. Again simply just stringing unrelated assertion together like “X is a beginning-only point exactly because no Y is comparable with it” does not make them related assertions.


doronshadmi said:
EDIT: You do not understand that each time that you compare Y (which is not X) with X, you get a closed form of finite amount of points.
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You do not understand that you have demonstrated no such limitation on comparison. If you want to assert such a limitation for your notions, fine, but it limits only you and makes your claims that “X is a beginning-only point” simply baseless by your own assertions and that limitation.
 
doronshadmi said:
X is the beginning AND an end point of each closed form.

All we have to do is to visit each point no more than twice (one visit is called beginning and the other visit is called end and it is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152).
Click to expand...

Which visit is called the "beginning", remember order did not matter for your “closed curve”?




doronshadmi said:
In the case of an infinite collection the arbitrary beginning X point of a closed form is visited only once.
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Which you can only distinguish as a beginning or an end if you are going to assert some ordering in your "visits".

For example the interval (X,Y] has Y as an included boundary (your end) but no other included boundary (your beginning).


If you claim that a beginning can be an end then your whole notion goes up in smoke as any beginning would also be an end.


Also you have yet to show how any of this limits the elements in a collection to some finite value, other then simply in your imagination.
 
The Man said:
If you claim that a beginning can be an end then your whole notion goes up in smoke as any beginning would also be an end.
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No smoke, simply a finite collection if any arbitrary beginning is also the end of the given collection of distinct elements.

This is not the case with an infinite collection of distinct elements.
 
The Man said:
For example the interval (X,Y] has Y as an included boundary (your end) but no other included boundary (your beginning).
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It does not matter if Y is (beginning AND end point) OR (end AND beginning point) of the given collection, and this case holds only if the collection is finite.

This is not the case with an infinite collection, where the arbitrary chosen point is beginning XOR end of the given collection.
 
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The Man said:
Which visit is called the "beginning", remember order did not matter for your “closed curve”?
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Any arbitrary point of the given collection of distinct points, is at least a beginning or an end point of that collection.

The Man said:
You do not understand that you have demonstrated no such limitation on comparison.
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No The Man, you simply can’t get the abstraction of http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 representation.
 
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The Man said:
Nope, until you define what constitute a “beginning AND an end” you have no basis to claim that aspect is limited to only a finite collection.
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In the case of a finite collection of distinct points, each point is at least both a beginning AND an end point of that collection.

This is not the case with an infinite collection of distinct points, because any arbitrary end or beginning point of that collection is not both a (beginning AND end point) OR (end AND beginning point) of the considered infinite collection.
 
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Let us look at these two diagrams:
4299700185_68a31d979e_o.jpg

We can clearly see that any point of a finite sub-collection of points of a given collection is both a beginning AND an end of the given finite sub-collection.

In the example above we see finite sub collections of one point for each sub-collection, and finite sub collections of two points for each sub-collection.

But the definition that determines that no arbitrary point of a given infinite collection is both a beginning AND an end of that collection, is not based on the finite sub-collections of the considered collection.

This is, for example, the reason of why The Man’s argument (http://www.internationalskeptics.com/forums/showpost.php?p=5543748&postcount=8159) about the inequality of each Y with X does not hold, because The Man’s case is based on infinitely many finite cases of two elements for each case (one for X and one for some Y that is not X) as can be seen in the right diagram.
 
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doronshadmi said:
No smoke, simply a finite collection if any arbitrary beginning is also the end of the given collection of distinct elements.

This is not the case with an infinite collection of distinct elements.
Click to expand...

Again a claim you have yet to demonstrate. Your assertion is apparently that if you simply ignore an “end” your collection mystically becomes infinite. Yet should you add a boundary point to your “infinite collection” it suddenly and mystically becomes your “finite collection”. So tell us Doron how does the addition of another point to an infinite collection of points suddenly make that collection finite?




doronshadmi said:
It does not matter if Y is (beginning AND end point) OR (end AND beginning point) of the given collection, and this case holds only if the collection is finite.

This is not the case with an infinite collection, where the arbitrary chosen point is beginning XOR end of the given collection.
Click to expand...

Again if you can not distinguish between the two (your beginning and your end) then any beginning is also your end and in fact a beginning is an end as nothing precedes it. It is the end of precession within the collection.


doronshadmi said:
Any arbitrary point of the given collection of distinct points, is at least a beginning or an end point of that collection.
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Again as you have not defined what constitutes your “beginning or an end” for any collection, your assertion remains without any merit.


doronshadmi said:
No The Man, you simply can’t get the abstraction of http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 representation.
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Your graphics demonstrate no limitation on comparison and if your are claiming that such a limitation is an “abstraction of http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 representation.” Then you are claiming that your graphics demonstrate no limitation on comparison.

doronshadmi said:
In the case of a finite collection of distinct points, each point is at least both a beginning AND an end point of that collection.


This is not the case with an infinite collection of distinct points, because any arbitrary end or beginning point of that collection is not both a (beginning AND end point) OR (end AND beginning point) of the considered infinite collection.
Click to expand...


Again simply repeating your baseless assertions do not give them any merit and in fact tends to confirm that you understand them as meritless since you will not provide a definition establishing what constitutes an “end or beginning point of that collection”.




doronshadmi said:
Let us look at these two diagrams:
[qimg]http://farm5.static.flickr.com/4062/4299700185_68a31d979e_o.jpg[/qimg]
We can clearly see that any point of a finite sub-collection of points of a given collection is both a beginning AND an end of the given finite sub-collection.
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Nope as you have not defined what constitutes a “beginning AND an end point of that collection” you have no basis to even assert that your collection has either a “beginning”, “end” or both.


doronshadmi said:
In the example above we see finite sub collections of one point for each sub-collection, and finite sub collections of two points for each sub-collection.
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Simple gibberish

doronshadmi said:
But the definition that determines that no arbitrary point of a given infinite collection is both a beginning AND an end of that collection, is not based on the finite sub-collections of the considered collection.
Click to expand...

Doron you have no “definition that determines that no arbitrary point of a given infinite collection is both a beginning AND an end of that collection” since you have no definition that determines what constitutes “a beginning” or “an end” for any given collection.



doronshadmi said:
This is, for example, the reason of why The Man’s argument (http://www.internationalskeptics.com/forums/showpost.php?p=5543748&postcount=8159) about the inequality of each Y with X does not hold, because The Man’s case is based on infinitely many finite cases of two elements for each case (one for X and one for some Y that is not X) as can be seen in the right diagram.
Click to expand...


Doron it was your argument “about the inequality of each Y with X” that does not hold since you claim you can not compare them in an infinite collection. Do not try to pawn off your own failed arguments onto others. So you are claiming now that you can compare “each Y with X” if it is “infinitely many finite cases of two elements for each case” which of course would be an infinite collection. So you're simply trying to abandon your previous assertions that


doronshadmi said:
If X and Y are compared, you get a finite collection.

So if the collection is infinite than X and Y are not compared.
Click to expand...

And backpedal your way away from them now?


Your assertion now is that any two elements can be compared even in an infinite collection thus "all" elements in that infinite collection can be compared. What happened to your limitation on comparison that you claimed was “the abstraction of http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152 representation”?
 
The Man said:
Your graphics demonstrate no limitation on comparison
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Because you can't get the difference between finite and infinite collections.

The Man said:
Your assertion now is that any two elements can be compared even in an infinite collection thus "all" elements in that infinite collection can be compared.
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Any finite sub-collection of points is comparable, such that each end or beginning arbitrary chosen point of a finite collection is visited twice.

This is not the case among an infinite collection of points, simply because the end or beginning arbitrary chosen point of an infinite collection is visited only once.

Your replies simply demonstrate that you can't grasp this fact, The Man, no matter if it is written or drawn.

The Man said:
Simple gibberish
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Yes I know, this is your best understanding of this fine subject.

The Man said:
Again a claim you have yet to demonstrate.
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Clearly demonstrated, whether you get is or not.
 
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So many, many posts, Doron, and nothing of substance.

You have proven you misunderstand Mathematics in general, and logic (especially logic!), set theory, geometry, topology, and algebra in particular. You have repeatedly presented contradictory claims, even within a single sentence. Your arguments are mostly universally circular.

You resort to outright lies to divert valid criticism. You even called your one and only supporter in the whole wide world a fool in this very forum.

And through all of this, what have you accomplished? Absolutely nothing.

You whole organic mathematics has no utility. It doesn't bridge any gap between ethics and science despite your claims. It cannot even produce a consistent result.

So, why do you bother with this idiocy, doron?
 
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doronshadmi said:
Because you can't get the difference between finite and infinite collections.
Click to expand...

I know the difference and you have still not demonstrated any limitation on comparison. Again if you simply want to claim that you can not compare elements in an infinite collection then that is just a limitation on your part and severely hampers your OM.


doronshadmi said:
Any finite sub-collection of points is comparable, such that each end or beginning arbitrary chosen point of a finite collection is visited twice.


This is not the case among an infinite collection of points, simply because the end or beginning arbitrary chosen point of an infinite collection is visited only once.
Click to expand...


As you have not defined what constitutes “each end or beginning arbitrary chosen point” those references remain without any merit. Again how does ‘visiting’ some point twice (thereby increasing the number of points visited by one point) suddenly make an infinite collection of points into a finite collection of points? Until you can explained how adding an element to an infinite collection suddenly makes it a finite collection you are simply stuck in a conundrum of your own making.




doronshadmi said:
Your replies simply demonstrate that you can't grasp this fact, The Man, no matter if it is written or drawn.
Click to expand...

Your inability to define those “end or beginning” references you so want to depend upon clearly demonstrates that you simply can’t grasp those facts and references while expecting others to do it for you.

doronshadmi said:
Yes I know, this is your best understanding of this fine subject.
Click to expand...

A simple result of your best gibberish explanations “of this fine subject”.

doronshadmi said:
Clearly demonstrated, whether you get is or not.
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Well then you are admitting that it was not “Clearly demonstrated”. The only thing “Clearly demonstrated” is that you are still a bit confused about what is “Clearly demonstrated” and seem to feel that you simply claiming something constitutes said clear demonstration.
 
The Man said:
Again how does ‘visiting’ some point twice (thereby increasing the number of points visited by one point) suddenly make an infinite collection of points into a finite collection of points?
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No The Man, we do not increasing the number of infinitely many visits by one more visit and suddenly get a finite number of visits.

You simply do not get the fact that each point is visited twice only if it is a finite collection, where in an infinite collection this fact simply does not hold, no matter how many more visits are added.
 
doronshadmi said:
No The Man, we do not increasing the number of infinitely many visits by one more visit and suddenly get a finite number of visits.

You simply do not get the fact that each point is visited twice only if it is a finite collection, where in an infinite collection this fact simply does not hold, no matter how many more visits are added.
Click to expand...

This thread just gets funnier and funnier.
 
dafydd said:
doronshadmi said:
No The Man, we do not increasing the number of infinitely many visits by one more visit and suddenly get a finite number of visits.

You simply do not get the fact that each point is visited twice only if it is a finite collection, where in an infinite collection this fact simply does not hold, no matter how many more visits are added.
Click to expand...

This thread just gets funnier and funnier.
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Indeed dafydd.

Doron, that you apparently do not support or even understand your own assertions is nothing new on this thread and is one of the things that makes this thread such a laugh riot.


Let’s go through this slowly for you. You have already asserted that to label every point along your “closed curve” would require an infinite number of n values (as labels). Thus a collection of those values would be an infinite set with each point being “visited” (for labeling) only once. We now label one of those points again (n,n) so at least one point has been “visited” (labeled) twice. By your assertions the collection of labels is now finite since some point was “visited” (labeled) twice, even though we have simply added an additional element to what you have stated is an infinite collection. As I have said before Doron if you do not like the results of your own assertions, then try to make better assertions
 
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The Man said:
Let’s go through this slowly for you. You have already asserted that to label every point along your “closed curve” would require an infinite number of n values (as labels). Thus a collection of those values would be an infinite set with each point being “visited” (for labeling) only once. We now label one of those points again (n,n) so at least one point has been “visited” (labeled) twice. By your assertions the collection of labels is now finite since some point was “visited” (labeled) twice, even though we have simply added an additional element to what you have stated is an infinite collection. As I have said before Doron if you do not like the results of your own assertions, then try to make better assertions
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Ah, but Doron doesn't seem to believe these point exist, despite him having a specified a curve somehow, until he labels them.
 
The Man said:
Indeed dafydd.

Doron, that you apparently do not support or even understand your own assertions is nothing new on this thread and is one of the things that makes this thread such a laugh riot.


Let’s go through this slowly for you. You have already asserted that to label every point along your “closed curve” would require an infinite number of n values (as labels). Thus a collection of those values would be an infinite set with each point being “visited” (for labeling) only once. We now label one of those points again (n,n) so at least one point has been “visited” (labeled) twice. By your assertions the collection of labels is now finite since some point was “visited” (labeled) twice, even though we have simply added an additional element to what you have stated is an infinite collection. As I have said before Doron if you do not like the results of your own assertions, then try to make better assertions
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I can follow that Doron,and I have only high school maths.Why can't you?
 
doronshadmi said:
Because you can't get non-locality, and you don't get the difference between atomic and complex states.
Click to expand...

You really need to stop blaming everyone else for your failings.


What exactly prevents from you to get a primitive thing like a pointless closed curve, for example?
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Would that be the very same pointless closed curve upon which you keep finding points? What exactly prevents "from you to get"[sic] a contradiction?
 
zooterkin said:
Ah, but Doron doesn't seem to believe these point exist, despite him having a specified a curve somehow, until he labels them.
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Also apparently why he thinks the points have to be "visited". He still seems stuck in some physical interpretation where an infinite set would require some infinite activity like "visiting" or “collecting”. Ironically he repeatedly accuses other people of lacking 'abstraction ability'.
 
The Man said:
Also apparently why he thinks the points have to be "visited". He still seems stuck in some physical interpretation where an infinite set would require some infinite activity like "visiting" or “collecting”.
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Exactly. I think this is why he has a problem with 'all' for an infinite set; he wants to make a list before he can be sure he has all of them.
 
zooterkin said:
Exactly. I think this is why he has a problem with 'all' for an infinite set; he wants to make a list before he can be sure he has all of them.
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You will notice though that he didn't even give "every" a second glance, but when I used the word "all" again he had his usual distain. So it is not the meaning of the word, as "every" means the same as "all" in those applications, but just some peculiar distain he just has for the word “all”. Tough I do agree that it most likely stems for this apparent fixation he seems to have with a collection, particularly an infinite collection, needing to be actually in some active and on going way collected, thus the infinite collection is never complete since the act of collecting continues infinitely.
 
The Man said:
You will notice though that he didn't even give "every" a second glance, but when I used the word "all" again he had his usual distain. So it is not the meaning of the word, as "every" means the same as "all" in those applications, but just some peculiar distain he just has for the word “all”. Tough I do agree that it most likely stems for this apparent fixation he seems to have with a collection, particularly an infinite collection, needing to be actually in some active and on going way collected, thus the infinite collection is never complete since the act of collecting continues infinitely.
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Bolding mine.

Yes. I've noticed this in Doron's polemic.
But at the same time he asserts more than just a potential infinity.
The Infinite is the Non-Local, ontologically present as one of the "building blocks" of his Organic Numbers. The range of the infinite is fully, undividebly present for every set, though it can't be called a completion of "all" points.
It's a bottomless well you can just keep pulling numbers out of.

Doron would not have you use the word "complete" regarding it, but as a fundamental "Atom," it is full and self contained.
The well cannot be emptied and with each bucket raised, it's still full.

But I've not called Doron on this contradiction of a fullness that is incomplete,
because it's a paradox inherent to the concept of infinity.

Doron to escape this paradox, presents the infinite as a seamless circle, or an unbounded line, having no individual points.
Non-Locality is a seamless whole having no individual parts. And that is Infinity in Doron's book.

Except that is not quite all of what we (including Doron) mean when we spaek of the concept of infinity. Again it's that we can go on and on and on, without ceasing. marking off points that designate numbers.
We can never "collect" all the points to infinity, because Infinity is always and ever whole.
The mind, nevertheless regards the Infinite as fundamentally Complete of itself, beyond loss or gain.

The classic way to escape this mental paradox is to assert as Aristotle or Kronecker that Infinity has no actual existence but is a mere direction of potentiality, and that it can't be thought of as a self-contained unit.

This, however is not Doron's approach.
It has to be that "ontological," "atomic," "building block."
Which brings with it that messy paradox, however it might be swept under the carpet and rolled under the couch.
 
Apathia said:
Bolding mine.

Yes. I've noticed this in Doron's polemic.
But at the same time he asserts more than just a potential infinity.
The Infinite is the Non-Local, ontologically present as one of the "building blocks" of his Organic Numbers. The range of the infinite is fully, undividebly present for every set, though it can't be called a completion of "all" points.
It's a bottomless well you can just keep pulling numbers out of.

Doron would not have you use the word "complete" regarding it, but as a fundamental "Atom," it is full and self contained.
The well cannot be emptied and with each bucket raised, it's still full.

But I've not called Doron on this contradiction of a fullness that is incomplete,
because it's a paradox inherent to the concept of infinity.

Doron to escape this paradox, presents the infinite as a seamless circle, or an unbounded line, having no individual points.
Non-Locality is a seamless whole having no individual parts. And that is Infinity in Doron's book.

Except that is not quite all of what we (including Doron) mean when we spaek of the concept of infinity. Again it's that we can go on and on and on, without ceasing. marking off points that designate numbers.
We can never "collect" all the points to infinity, because Infinity is always and ever whole.
The mind, nevertheless regards the Infinite as fundamentally Complete of itself, beyond loss or gain.

The classic way to escape this mental paradox is to assert as Aristotle or Kronecker that Infinity has no actual existence but is a mere direction of potentiality, and that it can't be thought of as a self-contained unit.

This, however is not Doron's approach.
It has to be that "ontological," "atomic," "building block."
Which brings with it that messy paradox, however it might be swept under the carpet and rolled under the couch.
Click to expand...


Bolding mine.


Ah yes the infinite ability of abstraction, with the added bonus of actual physical applications. We can calculate the magnitude and direction of a single vector at some point and the results of a vector field in some space. One of the results of which is our modern technological society.
 
The Man said:
Also apparently why he thinks the points have to be "visited". He still seems stuck in some physical interpretation where an infinite set would require some infinite activity like "visiting" or “collecting”. Ironically he repeatedly accuses other people of lacking 'abstraction ability'.
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Wrong interpretation. Collection, whether is is finite or not, does not need any activity. It simply a complex that can't be an atom.


Here is a little game.

It is called "The Source\Target Game".

It is played along a closed curve as follows:

1) The closed curve is the playground even if no player is found along it.

2) The players are points, such that each point is a source of one and only one target along the closed curve.

3) The first priority is given to the case where the source is not also the target, but if this is the only possibility than the source can be also the target (which is the second priority).

4) The game is completed only if each point is both a source AND a target.

Let's play:

a) If there are no players than there is no play, but it does not mean that there is no playground.

b) If there is exactly one player, then only the second priority is possible such that the source AND the target are the same player, and the game is completed.

c) If there is more than a one player then the first priority is possible.

By following the rules of this game, it is completed if there is a finite amount of players along the closed curve.

By following the rules of this game, please provide a proof that the game is completed (each point is source AND target) also if there is an infinite amount of players along the closed curve.
 
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Apathia said:
Which brings with it that messy paradox, however it might be swept under the carpet and rolled under the couch.
Click to expand...

There is no paradox simply because a complex (a closed curve with points a long it) is not an atom (a pointless closed curve).
 
The Man said:
Bolding mine.


Ah yes the infinite ability of abstraction, with the added bonus of actual physical applications. We can calculate the magnitude and direction of a single vector at some point and the results of a vector field in some space. One of the results of which is our modern technological society.
Click to expand...

Your results are valid (according to the current understanding of what is called actual physical realm) only if they are finite.
 
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doronshadmi said:
Wrong interpretation. Collection, whether is is finite or not, does not need any activity. It simply a complex that can't be an atom.


Here is a little game.

It is called "The Source\Target Game".

It is played along a closed curve as follows:

1) The closed curve is the playground even if no player is found along it.

2) The players are points, such that each point is a source of one and only one target along the closed curve.

3) The first priority is given to the case where the source is not also the target, but if this is the only possibility than the source can be also the target (which is the second priority).

4) The game is completed only if each point is both a source AND a target.

Let's play:

a) If there are no players than there is no play, but it does not mean that there is no playground.

b) If there is exactly one player, then only the second priority is possible such that the source AND the target are the same player, and the game is completed.

c) If there is more than a one player then the first priority is possible.

By following the rules of this game, it is completed if there is a finite amount of players along the closed curve.

By following the rules of this game, please provide a proof that the game is completed (each point is source AND target) also if there is an infinite amount of players along the closed curve.
Click to expand...

Please identify the point that is not a source for some other point and a target of some other point. Without that, each point is both “source AND target” your “game” does not even need to start. That’s what keeps your gaming going, once you start it, that every point is always a target and also a source for some other point.


Please insert quarters to start the game.

Thank You.

Game Over.

Please insert more quarters and play again.



Again we see Doron’s insistence on some type of activity like “visiting”, “collecting” and now “gaming” to infer that since an infinite activity continues an infinite set must be incomplete.
 
doronshadmi said:
Your results are valid (according to the current understanding of what is called actual physical realm) only if they are finite.
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The combination of two vector fields results in a new vector field, an infinite collection of vectors (in case you simply do not understand what a vector field is). The sum of an infinite number of finite lengths results in an infinite length. You are the only one claiming that infinite result is not valid. Your results and imagination of what you call “the current understanding” simply remain invalid.
 
The Man said:
Please identify the point that is not a source for some other point and a target of some other point.
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The first arbitrary point is a source for some other point but not a target of any other point if the collection along the closed curve is infinite.

Since you disagree with this simple fact, then please show how the first arbitrary point is also a target of some other point even if the collection along the closed curve is infinite.

The Man said:
once you start it, that every point is always a target and also a source for some other point.
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Worng.

Once I strat it, the first point is a source for another point but it is not a target for another point if the collection of points along the closed curve is infinite.

This is a fact exactly because there is always a target point (which is not the first point) along the curve, which blocks the first point from being a target for some source point (which is not the first point) if the collection is infinite.

Your inability to get this fact is resulted by the illusion that there is a satisfied sum for an infinite collection.
 
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