Deeper than primes

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jsfisher said:
This needs a little more discussion since there is an outside possibility, however slim, that doron may learn something. Addition provides a good example of something that works differently when we deal with the infinite. Despite dorons assertions to the contrary, mathematics doesn't assume the infinite to be a simple extension of the finite.

Addition is commutative. In computing the sum of numbers in any finite set, it does not matter what order the additions take place. Commutativity guarantees the final sum will be the same regardless. (Compare that to subtraction, which is not commutative, and you'll find the order does very much matter.)

However, the same cannot be said for the addition over infinite sets. The Man asserted the sum of all integers is 0. His statement is true, but it rests on a hidden assumption about the presumed order in which the additions are made.

Consider these two summations:

0 + (1 + -1) + (2 + -2) + (3 + -3) + ...
(1 + 0) + (2 + -1) + (3 + -2) + (4 + -3) + ...

The first reduces to 0+0+0+... while the second, 1+1+1+.... Yet, both are a summation of all the integers. Depending on how things are arranged, you can get any integer result you like as the sum of all integers, or even an infinite sum if you so prefer.
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No, not actually I was not asserting an infinite series of operations or any particular order for the summation. In fact the lack of having to actually perform an infinite series of operations was part of the point. Even if you do have infinite additions of “1+1+1+....” the negatives are not done until the limit of -∞, so even an infinite series of adding ones can not exceed the already positive limit of +∞ of the set. In fact that is all the positive integers are, just an infinite series of adding ones. As the negative integers are just an infinite series of subtracting ones.




jsfisher said:
ETA: ...or no definite sum at all (meaning the partial summation oscillates).
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Exactly “the partial summation.”
 
The Man said:
...Exactly “the partial summation.”
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Well, since the infinite sum is generally taken as the limit as N approaches infinity of the sum of the first N terms, I have a different view on this than you.
 
doronshadmi said:
In other words you reply even if you have no clue with what you deal with, how "interesting".
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No in the exact words I used

The Man said:
I put no "or" or "xor" in your "rule (2)", what the heck are you talking about.
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So again Doron simply will not or can not explain what the heck he is talking about, how uninteresting and certainly not surprising.

doronshadmi said:
A closed curve is some non-local aspect of the atomic state, exactly as a point is a local aspect of the atomic state.

No points are required for a closed curve, unless all you get is locality, and indeed this is your case, you simply can't grasp the notion of non-locality and how there is a closed curve without even a single point along it.

Again, this is your abstraction problem, not mine, so you have to solve this problem between you and yourself.
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So you will not or simply can not define a “closed curve” without any referances to location or points as you claimed you could, how uninteresting and certainly not surprising.

doronshadmi said:
No, The Man by switching between source and target you only change direction, where the amount can be finite or infinite. Rule (2) is about the inability of a source to be a source for more than one target, and you violate it because you are using "or" instead of "xor".
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Again with this “"or" instead of "xor"”. Nonsense. Doron you are going to have to be specific, I know that is hard for you, but how is my using “or” in a simple discussion somehow a violation of your “Rule (2)”. If you somehow thing I’m trying to redefine your “Rule (2)” with "or" instead of "xor", then I have no idea how you got that misconception.

Again.


The Man said:
Nope reverse ordering simply changes a source to a target and a target to a source. It certainly does not increase the number a targets for any given source. What is does do is belie your ordering distinction between a source and a target that you try to maintain as a hidden assumption to assert that your “first arbitrary” point is a source but not a target.
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The Man said:
It is simply "amazing" that you can't get a single word of what you read (and as a result, also what you write).
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Doron you’re the one making the assertion like I’m “using "or" instead of "xor"” If you can not be clear about what you are saying then you just must not want people to understand what it is you are asserting.

The Man said:
Yes I know, that's exactly what happens in your head.
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No Doron all the struggling remains in your head.
 
jsfisher said:
Well, since the infinite sum is generally taken as the limit as N approaches infinity of the sum of the first N terms, I have a different view on this than you.
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I was actually going to say "approaches +∞" as opposed to "of +∞", but it just seemed more consistent with the point I was trying to make and I doubt our views on this are all that much different.
 
doronshadmi said:
Since the phrase "all infinitely many ..." is a contradiction, and reals or integeres are infinite collections, that there is no such a thing like "the sum of all real numbers or all integers being 0".

It is true only if you deal with finite collections of reals or integers.
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“Since the phrase "all infinitely many ..." is a contradiction” only to you, then that is your problem and just another limitation of your OM.
 
doronshadmi said:
EDIT:

So you do have problems to grasp infinite interpolation\extrapolation, which is an example of infinite (and therefore incomplete) complexity.
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Again, doron, you try to rush ahead without establishing any sort of foundation. Patience.

Let's review: Finite sets are complete and infinite sets are incomplete in doronetics. Without further distinction as to what you actually mean by these two terms, we have to conclude they are synonyms for finite and infinite. Complete and incomplete are extraneous concepts, therefore; they have no independent value.

Complexity is related to finite and infinite sets exactly as the complete/incomplete pair were. What can you add, doron, that will differentiate complexity? Or is complexity, whatever that means in doronetics, an extraneous concept as well?
 
The Man said:
Again a target but not a source is an ordering distinction, just as "first" is.
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There is a direction (no reverse within this game) exactly because any given source is a source for exactly one and only one target. Even though, the values along the game do not have any specific order (as clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152), they are simply distinct of each other.

If the first point is also a target in that game (according to rule (2) of this game), then the collection is called complete, and it is easily shown that it is possible only if there are finite points in this game.
 
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As for Real or integers, we can use also some order, for example:

0 is the first point and then we have pairs of negative and positive numbers (for example: –x,x,-y,y,-z,z, … etc.).

Still 0 is not a target of any other real or integer number , if the collection or real or integer numbers along the closed curve, is infinite.


So order has no significance in this game. All we care is if the first element is also a target, or not.


Only distinction matters in this game, and from this general view only finite collections are also complete.
 
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jsfisher said:
Again, doron, you try to rush ahead without establishing any sort of foundation. Patience.

Let's review: Finite sets are complete and infinite sets are incomplete in doronetics. Without further distinction as to what you actually mean by these two terms, we have to conclude they are synonyms for finite and infinite. Complete and incomplete are extraneous concepts, therefore; they have no independent value.

Complexity is related to finite and infinite sets exactly as the complete/incomplete pair were. What can you add, doron, that will differentiate complexity? Or is complexity, whatever that means in doronetics, an extraneous concept as well?
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Very simple.

A complex is complete only if it has a finite amount of elements.

A complex is incomplete only if it has an infinite amount of elements.

For example: the complex 0_.222...[base 3] is incomplete, and it is different from the complex 0_.111...[base 2], which is also incomplete.

Both of them are different than the complex 0_1 which is complete, as clearly seen in:

4318895416_366312cf0e_o.jpg


The non-local numbers (which is a new thing) are born.

EDIT:

(0_1 - 0_.222...[base 3] = 0_.000...1[base 3]) < (0_1 - 0_.111...[base 2] = 0_.000...1[base 2])
 
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doronshadmi said:
There is a direction (no reverse within this game) exactly because any given source is a source for exactly one and only one target.
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Again reversing the ordering does not increase the number of targets for each source. So your “exactly because any given source is a source for exactly one and only one target” is not a restriction on reverse ordering. If you want to claim now that “There is a direction (no reverse within this game)” then you have just added a new rule to your “game”. Also that there is a direction (by your own assertions) also means there is an opposite direction (no reverse ordering required) and again if you can identify a target for your first point in the infinite collection of points then in the opposite direction along your “closed curve” is a similar point that your first point is a target of. Again the same aspect that you depend upon to keep your first point from being a target in the infinite collection also keeps it from having a target in that collection. We can keep going around this same “closed curve” Doron, but you will still never get anywhere.

doronshadmi said:
Even though, the values along the game do not have any specific order (as clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5542852&postcount=8152), they are simply distinct of each other.
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You do have a specific order, source to target, that you are trying to re-enforce with your new “(no reverse within this game)” rule, since a source is just a target in reverse order. Also none of this changes the fact that you are claiming your first point is source but not a target which is specifically an ordering distinction just as “first” is. Again this completely belies your claim of “the values along the game do not have any specific order”. If that were true then your first point couldn’t be any different then your second, third or forth, technically there would be no “first” other then a simple and basically meaningless label of “first” that one might apply. Since you simply want to label some point as “first” that label should carry no particular distinctions along your “closed curve”, but you insist that it does and that your “first” point carries the specific and unique ordering distinction form all other points along your “closed curve” of being a source but not a target. Your whole premise is about giving just one point a specific and unique ordering distinction simply by you labeling it as “first”.

Once again your requirement for a closed curve places its own ordering restrictions on any points along that curve, specifically that any point is both a predecessor and successor to any point along that closed curve, including itself.


doronshadmi said:
If the first point is also a target in that game (according to rule (2) of this game), then the collection is called complete, and it is easily shown that it is possible only if there are finite points in this game.
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Again if your “first point” is a source then it is also a target and in fact it must be an obtainable target of your “closed curve” in general otherwise your “curve” is not closed. So it really doesn’t matter what point your “first point” is a target of, if it is simply not an obtainable target of some point along your “closed curve”, including itself, then your “closed curve” is simply not closed. It is your own requirement for a “closed curve” as your “playground” that concludes your “game”

Got that pointless “closed curve” definition yet?
 
doronshadmi said:
Very simple.
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If it is so simple, how is it that you are having such difficulty differentiating among the concepts?

A complex is complete only if it has a finite amount of elements.

A complex is incomplete only if it has an infinite amount of elements.
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Case in point. From what you have written, complexity, complete, and finite are all the same thing.

That makes your whole wad of concepts extraneous. You have substituting words pretending to have infused new meaning, but you didn't. You've just moved laterally.


Now, take a breath, relax, and try again. Notice I haven't asked you to actually define complete, for example. You have no demonstrated ability to define anything, so I wasn't expecting that to change now. However, I am asking you to differentiate between complete and finite, and between complexity and complete.

Can you do that, or are they really synonyms?
 
doronshadmi said:
As for Real or integers, we can use also some order, for example:

0 is the first point and then we have pairs of negative and positive numbers (for example: –x,x,-y,y,-z,z, … etc.).

Still 0 is not a target of any other real or integer number , if the collection or real or integer numbers along the closed curve, is infinite.


So order has no significance in this game. All we care is if the first element is also a target, or not.


Only distinction matters in this game, and from this general view only finite collections are also complete.
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The good thing about integers is that we can establish an immediate predecessor and an immediate successor for some point that one simply can not define in the reals. With 0 as your first point its immediate successor (or target) is +1 making it immediate predecessor (or source) as -1. Again Doron you simply want to claim that your “first point” has a successor (target) but no predecessor (source) while your assertion of a closed curve requires that every point be both a predecessor (source) and successor (target) of every point along your “closed curve” including itself.
 
Doron your “new model of the infinite simply” boils down to you labeling the points along your “closed curve”. Sure you can label some point first, another second, then third, fourth, fifth…, but a list of those label can never be completed. Fortunately all we have to do is establish a rule for labeling the points and a collection of those labels is definable and complete. You have gone out of your way and wasted your time trying to dress up the fact that an infinite list can not be completed as some “new model of the infinite”.
 
The Man said:
Again reversing the ordering does not increase the number of targets for each source.
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Only if there is a xor between some direction and its reverse.

You clearly used or (here: http://www.internationalskeptics.com/forums/showpost.php?p=5561167&postcount=8212 and here: http://www.internationalskeptics.com/forums/showpost.php?p=5564918&postcount=8227) instead of xor, and as a result a source can have more than one target if cardinality > 2.

In other words, you do not follow the rules of the game and as a result you can't distinguish between finite and complete collection of points along a closed curve (each point is both a source AND a target) and between infinite and incomplete collection (the first point is not a target) along a closed curve.

Again, a closed curve has nothing to do with the points along it, because there is a pointless closed curve in this game.


The Man said:
The good thing about integers is that we can establish an immediate predecessor and an immediate successor for some point that one simply can not define in the reals.
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In both cases the first point is not a target if the collection is infinite.


The Man said:
Fortunately all we have to do is establish a rule for labeling the points and a collection of those labels is definable and complete.
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Please show us how an infinite collection of points along a closed curve is complete (the first point is also a target), such that each point is a source for one and only one target.
 
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jsfisher said:
I am asking you to differentiate between complete and finite, and between complexity and complete.

Can you do that, or are they really synonyms?
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Come on jsfisher, a complex can be complete (has finitely many elements) or incomplete (has infinitely many elements).

So simple to understand and clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5553203&postcount=8194 and http://www.internationalskeptics.com/forums/showpost.php?p=5569905&postcount=8290.
 
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doronshadmi said:
Only if there is a xor between some direction and its reverse.
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A specific ordering excludes other orderings your “xor” is superfluous. A particular direction dictates the other direction as its reverse again your “xor” is superfluous. Again reverse ordering (changing source to target) does not itself change the number of targets for each source, it just changes a source to a target, so you can do whatever you want with your “xor”.

doronshadmi said:
You clearly used or instead of xor, and as a result a source can have more than one target if cardinality > 2.
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Again reverse ordering (changing source to target) does not itself change the number of targets for each source, it just changes a source to a target, so you can do whatever you want with your “xor”.

Reverse ordering and just looking in the other direction for a source are not mutually exclusive and neither of them, independently or together, change the number of targets for each source. They do however belie your ordering distinction to claim that your first point is a source but not a target.


doronshadmi said:
In other words, you do not follow the rules of the game and as a result you can't distinguish between finite and complete collection of points along a closed curve (each point is both a source AND a target) and between infinite and incomplete collection (the first point is not a target) along a closed curve.
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Again reverse ordering (changing source to target) does not itself change the number of targets for each source, it just changes a source to a target, so you can do whatever you want with your “xor”. Again if you can find a target for your first point in the infinite collection then in the opposite direction along your closed curve there is a similar point that has your first point as a target. Again the very aspect (an infinite collection of points) that you depend on to keep your first point from being a target also keeps it from having a target.

Again doron we can keep going around this “closed curve” all you want but it will still get you nowhere.



doronshadmi said:
Again, a closed curve has nothing to do with the points along it, because there is a pointless closed curve in our game.
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Good so you’ve finally got that definition of a “pointless closed curve”, let’s hear it.


doronshadmi said:
Please show us how an infinite collection of points along a closed curve is complete (the first point is also a target), such that each point is a source for one and only one target.
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Because your “closed curve” is complete, if it isn’t then it just ain’t closed.

Again please tell us how removing one element (your first point) from the infinite set of points to make your set of targets somehow makes that set finite or just not infinite?
 
doronshadmi said:
Very simple.

A complex is complete only if it has a finite amount of elements.

A complex is incomplete only if it has an infinite amount of elements.

For example: the complex 0_.222...[base 3] is incomplete, and it is different from the complex 0_.111...[base 2], which is also incomplete.

Both of them are different than the complex 0_1 which is complete, as clearly seen in:

[qimg]http://farm3.static.flickr.com/2793/4318895416_366312cf0e_o.jpg[/qimg]

The non-local numbers (which is a new thing) are born.

EDIT:

(0_1 - 0_.222...[base 3] = 0_.000...1[base 3]) < (0_1 - 0_.111...[base 2] = 0_.000...1[base 2])
Click to expand...


What? “A complex is incomplete only if it has an infinite amount of elements” so for the set of all integers {-1, 5} is complete because it is finite even thought it is missing every integer but two?

Doron again you are simply attempting to redefine complete to mean finite and incomplete mean infinite. This may surprise you but we already have words to indicate finite and infinite and by some strange coincidence they just happen to be “finite” and “infinite”. This happens to be a big help so people can actually understand what you are trying to say.
 
doronshadmi said:
Come on jsfisher, a complex can be complete (has finitely many elements) or incomplete (has infinitely many elements).
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I did not ask you what a complex can and cannot be. I asked you to differentiate between complexity and completeness. If complexity and complex are unrelated terms, we can table that and just focus on my other questions, how do you differentiate between incomplete and infinite.

This should not be difficult. If the terms are truly different, they must refer to different characteristics. Please clarify the distinctions among the terms.
 
The Man said:
What? “A complex is incomplete only if it has an infinite amount of elements” so for the set of all integers {-1, 5} is complete because it is finite even thought it is missing every integer but two?

Doron again you are simply attempting to redefine complete to mean finite and incomplete mean infinite. This may surprise you but we already have words to indicate finite and infinite and by some strange coincidence they just happen to be “finite” and “infinite”. This happens to be a big help so people can actually understand what you are trying to say.
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As I have said, a collection is a complex.

A complete complex is finite.

An incomplete complex is infinite.

Since you do not understand that a collection is a complex, you wrongly understand the difference betweeen the finite and the infinite.

EDIT:

The Man, again your view about collections is limited to the particular case where the number of classes < the number of elements of a given collection.

OM is focused only on distinction, where the number of classes has no significance (it can be < or = to the number of the elements of a given collection).

In other words, OM's notion is a generalization of the current paradigm about collections.

Also you do not grasp yet the beauty of http://www.internationalskeptics.com/forums/showpost.php?p=5563876&postcount=8224.
 
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The Man said:
Again reverse ordering (changing source to target) does not itself change the number of targets for each source,
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Still the first source is not a target if the collection is infinite.

The problem is that you and jsfisher do not understand what a collection is.
 
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doronshadmi said:
As I have said, a collection is a complex.

A complete complex is finite.

An incomplete complex is infinite.

Since you do not understand that a collection is a complex, you wrongly understand the difference betweeen the finite and the infinite.
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That's rich,coming from you.
 
doronshadmi said:
Still the first source is not a target if the collection is infinite.

The problem is that you and jsfisher do not understand what a collection is.
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Nonsense. The problem is you don't understand what a synonym is. Making up new words for old, which is all you have done, does not a new paradigm create.

All you have done is use complex where you should be using collection and complete where finite belongs. Your intent is to obscure, not to communicate.
 
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Given the mountain of ingnorance that the real mathematicians face here,this thread may turn out to be infinite.
 
doronshadmi said:
OM is focused only on distinction, where the number of classes has no significance (it can be < or = to the number of the elements of a given collection).
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Bolding mine.

Only?
Ah, can't you at least throw mathematicians a few peanuts.
At least that numbers as they know them are a special case of OM?
I thought before that you'd said (in so many words) that you weren't abolishing deductive reasoning but putting it in its wider context. :wackyv_SPIN:
 
Apathia said:
Bolding mine.

Only?
Ah, can't you at least throw mathematicians a few peanuts.
At least that numbers as they know them are a special case of OM?
I thought before that you'd said (in so many words) that you weren't abolishing deductive reasoning but putting it in its wider context. :wackyv_SPIN:
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If you wish to understand the difference between finite and infinite collections you must get the notion of collection from the most general view.

By using only Distinction (which is not limited by the concept of class) you get the needed generalization in order to understand the difference between finite and infinite collection.

Exactly as Order has no impact on the cardinality of a given collection so is Class, and it becomes clearly understood when we go beyond Class and Order and use only Distinction.
 
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jsfisher said:
Nonsense. The problem is you don't understand what a synonym is. Making up new words for old, which is all you have done, does not a new paradigm create.

All you have done is use complex where you should be using collection and complete where finite belongs. Your intent is to obscure, not to communicate.
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Collection is a particular case of a complex, where only the first level of a complex is considered.

Since you do not understand Complexity you do not understand Collection.

One of the results of this misunderstanding is to get Collection only in terms of Class, such that the number of classes of a given collection < the number of the elements of a given collection.

As a result phrases like "show me the missing natural number of set N" are said, which clearly demonstrate that the view of the one who says this phrase is limited to the particular case, where the number of classes of a given collection < the number of the elements of that collection.

Under this limited view one can't get the generalization of the inability of the first element to be a target, if a given collection is infinite.
 
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doronshadmi said:
As a result phrases like "show me the missing natural number of set N" are said, which clearly demonstrates that the view of one who says this phrase is limited to the particular case, where the number of classes of a given collection < the number of the elements of that collection.
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No. You say that 'all' cannot be applied to an infinite set. You have been asked to state which member is missing when I refer to "all the positive integers".
 
zooterkin said:
No. You say that 'all' cannot be applied to an infinite set. You have been asked to state which member is missing when I refer to "all the positive integers".
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Which is a question that is limited to the particular case, where the number of classes < the number of the elements of a given collection.
 
doronshadmi said:
Collection is a particular case of a complex, where only the first level of a complex is considered.
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So, by their omission you are conceding complete and finite are synonyms. Fine. All that is left for you to stop evading is distinguishing between collection and complex in a meaningful way. Simply saying "first level" doesn't hack it unless you can somehow manage to define what that means.

How about an example of a complex that isn't a collection?
 
jsfisher said:
So, by their omission you are conceding complete and finite are synonyms. Fine. All that is left for you to stop evading is distinguishing between collection and complex in a meaningful way. Simply saying "first level" doesn't hack it unless you can somehow manage to define what that means.

How about an example of a complex that isn't a collection?
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When also the internal structure of a given element of some collection, is taken.

But you have missed the generalization by Distinction that has been written in http://www.internationalskeptics.com/forums/showpost.php?p=5573325&postcount=8309 , where in this case the elements are points (have no internal structure) and still your notions about the concept of collection is limited to the particular case, where the number of classes < the number of the elements of some collection, in the case that you join to zooterkin's question.

So my question to you is: Do you join to Zooterkin's question (http://www.internationalskeptics.com/forums/showpost.php?p=5573341&postcount=8310)?
 
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doronshadmi said:
Still the first source is not a target if the collection is infinite.

The problem is that you and jsfisher do not understand what a collection is.
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Again if it can be a source then it can also be a target, also your requirement of a "closed curve" makes it an obtainable (in the set of) target(s) otherwise your "curve" simply isn't "closed".




doronshadmi said:
As I have said, a collection is a complex.

A complete complex is finite.

An incomplete complex is infinite.
Click to expand...

Again

The Man said:
so for the set of all integers {-1, 5} is complete because it is finite even thought it is missing every integer but two?
Click to expand...


doronshadmi said:
Since you do not understand that a collection is a complex, you wrongly understand the difference betweeen the finite and the infinite.
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Nope, one is finite and the other infinite, not hard at all. Good thing we have words that actually mean finite and infinite like, well, finite and infinite.


The Man said:
EDIT:

The Man, again your view about collections is limited to the particular case where the number of classes < the number of elements of a given collection.
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Doron your “view about collections” leads to the absolutely ridiculous conclusion that for the “collection” of all integers {-1, 5} is complete because it is finite even thought it is missing every integer but two.

The Man said:
OM is focused only on distinction, where the number of classes has no significance (it can be < or = to the number of the elements of a given collection).
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Doron whatever “OM is focused” on it is only in your mind and from your postings even that focus is extremely blurry.

The Man said:
In other words, OM's notion is a generalization of the current paradigm about collections.
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Again Doron “generalization” does not mean you simply making up whatever self-contradictory nonsensical gibberish that suits you.

The Man said:
Also you do not grasp yet the beauty of http://www.internationalskeptics.com/forums/showpost.php?p=5563876&postcount=8224.
Click to expand...

Again, because it is simply your fantasy.
 
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