Deeper than primes - Continuation

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doronshadmi said:
The traditional mathematicians here get ...11011... = ...10111... as the only possible option, and expose once again the limitation of their verbal_symbolic-only reasoning.
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What is the difference between ...11011... and ...10111...? Mind that I'm not asking about the difference between 11011 and 10111. That's an entirely different question.
 
One has to put ...10111... and ...11011... upon each other (an overlap) and he/she immediately see the difference.
 
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doronshadmi said:
One has to put ...10111... and ...11011... upon each other (an overlap) and he/she immediately see the difference.
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No, I specifically said that I'm not talking about 10111 and 11011. You can't put ...10111... and ...11011... upon each other, unless you assume that the dotted parts are exactly the same length.

So, again, what is the difference?
 
doronshadmi said:
I claimed...Well this claim is wrong...
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Excellent. One step forward.

......and since this is the case, my theorem in http://www.internationalskeptics.com/forums/showpost.php?p=8453947&postcount=1698 holds also in terms of verbal_symbolic-only reasoning.
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And two step back.

Ignoring the fact you still haven't recognized the need for a fixed reference point in your binary sequences for them to be in any way useful, you have the very basic problem that your alleged theorem fails at every single step.

Let's just assume, for the sake of moving things along, you have finally accepted the statement "No set is a member of itself" as your alleged theorem statement, and you have figured out that your (2) is not only wrong, but totally unnecessary, and you have figured out that your codes in (3) need a fixed reference, you still have yet another problem:

There are fewer unique codes then you need.

So, your step (3) fails before leaving the station, so we don't have to consider any of the fatal flaws in the steps that follow.
 
This is nice, by using verbal_symbolic only reasoning the traditional mathematicians here claim that ...10111... and ...11011... are the same sequence, but somehow they also claim that "there are fewer unique codes then you need" (which means that they look beyond the case of ..10111... = ...11011... in order to conclude that "there are fewer unique codes then you need").

This is a concrete example of a mind that is not aware of itself during its mathematical work.

This kind of mind can't say any meaningful thing about, for example, Flagg resolution as appears in Prof. Kauffman's work.

Also a simple thing like http://www.internationalskeptics.com/forums/showpost.php?p=8466068&postcount=1766 and http://www.internationalskeptics.com/forums/showpost.php?p=8466122&postcount=1768 is not in the scope of such mind.

One of the properties of such minds is that do not read the whole thing in order to understand it before they reply, but the reply is done separately to each part, for example"

Reply 1: "Excellent. One step forward."

Then reply 2: "And two step back."

No wonder that such minds can't really comprehend what is actually written.
 
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The doted parts are exactly the same length independently of the particular content of the arbitrarily chosen common location for both ...10111... and ...11011... unbounded sequences, for example:

Code: 
...10111...
     |
...11011...

where "|" is the arbitrarily chosen common location for both ...10111... and ...11011... unbounded sequences.
 
doronshadmi said:
The doted parts are exactly the same length independently of the particular content of the arbitrarily chosen common location for both ...10111... and ...11011... unbounded sequences, for example:

Code: 
...10111...
     |
...11011...

where "|" is the arbitrarily chosen common location for both ...10111... and ...11011... unbounded sequences.
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Arbitrarily? OK, I choose this one:

Code: 
...[B].[/B]10111...
     |
...11011[b].[/b]...

Where's the difference?
 
The first arbitrary choice is done between different unbounded sequences.

The second arbitrary choice is done between a given unbounded sequence and itself.
 
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doronshadmi said:
This is nice, by using verbal_symbolic only reasoning the traditional mathematicians here claim that ...10111... and ...11011... are the same sequence, but somehow they also claim that "there are fewer unique codes then you need" (which means that they look beyond the case of ..10111... = ...11011... in order to conclude that "there are fewer unique codes then you need").
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Yep, fewer unique codes than needed. You cannot produce codes for any set larger than the set of reals.

You are being shallow, Doron.
 
In addition to http://www.internationalskeptics.com/forums/showpost.php?p=8466122&postcount=1768 , if an arbitrary choice is done between two unbounded "0;1" sequences, such that both sides form the chosen place (have the same amount of symbols) AND (the same symbols) AND (the symbols at the arbitrarily chosen place are different), then the two unbounded binary sequences are unconditionally not the same unbounded binary sequence.
 
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By the "You cannot produce codes for any set larger than the set of reals." phrase, the traditional mathematicians here demonstrate their inability to comprehend the incompleteness of {..., ...10111..., ...11011..., ...} or P({..., ...10111..., ...11011..., ...}) or ...P(P({..., ...10111..., ...11011..., ...}))..., which shows that no infinite set has strict cardinality, or in other words, Cantor's transfinite universe does not hold, and this is exactly the subject of http://www.internationalskeptics.com/forums/showpost.php?p=8453947&postcount=1698.

The reals are nothing but an incomplete set of local numbers.
 
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I suppose the proof these latest restatements of previously uttered falsehoods is as convincing as all of your proofs, right?
 
The consistent evidence about the community of traditional mathematicians' reasoning is seen in http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694.

The one that said "put up or shut up" can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694 or http://www.internationalskeptics.com/forums/showpost.php?p=8466341&postcount=1770.

Also to say that "that's just gibberish, and hardly a useful result" clearly shows that this one does not understand the word "gibberish", simply because if something is taken as gibberish by someone, he simply can't claim that it is "hardly a useful result", because by getting something as gibberish one has no clue of what he gets as gibberish.

Let us make it simpler, instead of being honest and say "you do not understand what you say" this one calls to what I say "Nope, that's just gibberish", by repeating like a parrot after other posters here, which also have no clue of what I am talking about in http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694 or http://www.internationalskeptics.com/forums/showpost.php?p=8466341&postcount=1770.
 
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doronshadmi said:
The consistent evidence about the community of traditional mathematicians' reasoning is seen in http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694.

The one that said "put up or shut up" can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694 or http://www.internationalskeptics.com/forums/showpost.php?p=8466341&postcount=1770.

Also to say that "that's just gibberish, and hardly a useful result" clearly shows that this one does not understand the word "gibberish", simply because if something is taken as gibberish by someone, he simply can't claim that it is "hardly a useful result", because by getting something as gibberish one has no clue of what he gets as gibberish.

Let us make it simpler, instead of being honest and say "you do not understand what you say" this one calls to what I say "Nope, that's just gibberish", by repeating like a parrot after other posters here, which also have no clue of what I am talking about in http://www.internationalskeptics.com/forums/showpost.php?p=8452050&postcount=1694 or http://www.internationalskeptics.com/forums/showpost.php?p=8466341&postcount=1770.
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Translation: I got nothing. We hear you, doron, loud and clear. Just wanted to make sure.
 
This one actually can't "hear" his own reasoning (he does not have one to be heard), not to mention my reasoning, which is no more than gibberish (by his own deviance) for him.
 
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doronshadmi said:
This one actually can't "hear" his own reasoning (he does not have one to be heard), not to mention my reasoning, which is no more than gibberish (by his own deviance) for him.
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Sorry, care to rephrase that in English instead of Gibberish?
 
More about ...10111..., ...11011..., etc. forms.

If an overlap among such forms is used, we get the following results, which enable to distinguish between such forms, as follows:

...101... (self overlapping)

...1001... (this is the overlap result among ..10111..., ...11011...)

...10101...

...101101...

...1011101...

... etc. ad infinitum ...
 
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doronshadmi said:
More about ...10111..., ...11011..., etc. forms.
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Forms? You say that like you believe their format is what gives them meaning. That, my dear, was much the point of this particular exercise. The example expressed the identical sequence in two ever-so slightly different forms.

Circling back to the bogus proof you presented, you are still stuck at step #3 (and that's only after we assume you are able to correct the theorem statement, amend #1 accordingly, and jettison #2 as wrong but irrelevant). There is no general method to distinguish between two of your codes so to assert they are unique is an invalid claim.

Your proof remains a failure at every step.
 
Theorem:

There does not exist a set X such that if set X is a member of set U, then set X is identical to set U.

Proof:

(1) Let us suppose that there exists a set X such that if set X is a member of set U, then set X is identical to set U.

(2) Every member of set U is unique.

(3) According to (2) each member can be represented by a unique code, where in the case of infinite collection of members there is no first or last code, where each unique code is an infinitely long sequence of symbols without first or last symbol, for example:

{
...

...01001... ,
...11101... ,
...10110... ,
...11111... ,
...10101... ,
...

}

(4) The code of set U is defined by using Cantor's Diagonalization (without using any mapping between the members of two given sets), which is different than the other codes that represent its members (in this example the code of set U is ...10000...).

(In order to get a unique Cantor's Diagonalization code (in case that there is no first or last code, and also each code does not have first or last symbol) we arbitrarily choose some symbol of some arbitrary distinct code, and from there (by including the arbitrarily chosen symbol) we construct a complement "0;1" code by "moving" simultaneously from the arbitrarily chosen symbol infinitely many times (up AND left) AND (down AND right) by single steps).

(5) If set U is one of its own members, then its code (for example:...10000...) must appear in the collection of the unique codes, which represent the members of that set.

(6) But according to (4) the code of set U is defined by using Cantor's Diagonalization (without using any mapping between the members of two given sets), and in this case the code of set U is different than the codes of the members of set U (the example ...10000... can't be considered as the code of set U, if it is used as a code of a member of set U, because if ...10000... is considered as a code of a given member of set U, Cantor's Diagonalization code of set U, is different than that code by at least one symbol).

(7) According to (6) assumption (1) is false and we can conclude that there does not exist a set X such that if set X is a member of set U, then set X is identical to set U.

Q.E.D

The claim that, for example, ...10111... and ...11011..., are the same code, is false, because by using an overlap among such codes, we get the following results, which enable to distinguish between them, as follows:

...101... (self overlapping)

...1001... (this is the overlap result among ..10111... and ...11011... codes)

...10101...

...101101...

...1011101...

... etc. ad infinitum ...

The traditional mathematicians here get only the ...101... (self overlapping) case.
 
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doronshadmi said:
Theorem:

There does not exist a set X such that if set X is a member of set U, then set X is identical to set U.
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Ah!!! Finally, you amended the original gibberish to this. It's still contorted, but at least it isn't complete nonsense. Any reason you cannot go with the simpler statement, "No set is a member of itself"?

...
(2) Every member of set U is unique.
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Yeah? Prove it!

(3) According to (2) each member can be represented by a unique code
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Even if (2) were true, it wouldn't support this inference.

...where in the case of infinite collection of members there is no first or last code, where each unique code is an infinitely long sequence of symbols without first or last symbol
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And your nonsense proof continues to hit a hard stop. You haven't shown there are enough of your binary sequences to handle the larger sets. You haven't even established what it means for two sequences to be different from each other. (This latter short-coming would become vitally important in later steps, but you will have trouble moving past this one.)
 
doronshadmi said:
The claim that, for example, ...10111... and ...11011..., are the same code, is false
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The claim had to do with an unbounded series of 1's from the left, then a 0, then an unbounded series of 1's to the right. Such a sequence could be expressed as ...111011... or as ...110111... or as ...111111111101111111111... or as ....

In all cases, the notation is not the sequence; it is a tool for its expression.

In the example, then, ...111011... and ...110111... are (expressions for) the identical sequence.

...because by using an overlap among such codes....
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Perhaps you'd be so kind as to explain what you mean by "using an overlap among such codes". It looks like you are just aligning the sequences with each other in arbitrary ways then taking the bit-wise AND as the result.

That would be an indeterminate process used to derive a meaningless result.
 
In addition to the ability get only the ...101... (self overlapping) case, the traditional mathematicians here miss the difference between being a set (the members of a given non-empty set like U are unique) and being a multiset (where U is not a multiset).
 
Look at this phrase "Such a sequence could be expressed as ...111011... or as ...110111... or as ...111111111101111111111... or as ...."

According to this phrase we can clearly see how the traditional mathematicians here can't comprehend the difference between the codes, which are derived from the shifts among the codes that are paths of the same unbounded binary tree (they can't comprehend the Tree\paths relations).
 
doronshadmi said:
In addition to the ability get only the ...101... (self overlapping) case, the traditional mathematicians here miss the difference between being a set (the members of a given non-empty set like U are unique) and being a multiset (where U is not a multiset).
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Doron, since you have such a long and proud history of being totally incapable of defining any of your terms or explaining any of your bizarre reasoning, it is no surprise you come up empty again.

You cannot explain what you mean by "using overlap". We get that.
You cannot explain what relevance you see in "using overlap". We get that.
You cannot understand set theory beyond the conceptual abilities of a third grader. We get that, too.
 
doronshadmi said:
Look at this phrase "Such a sequence could be expressed as ...111011... or as ...110111... or as ...111111111101111111111... or as ...."

According to this phrase we can clearly see how the traditional mathematicians here can't comprehend the difference between the codes, which are derived from the shifts among the codes that are paths of the same unbounded binary tree (they can't comprehend the Tree\paths relations).
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You used the wrong pronoun. "We" is plural. You are singular in this continued projection.
 
Once again.

The traditional mathematicians here can't get the unbounded binary tree as a common universe of different paths, whether it is represented by the following diagram or by its equivalent set:

7595514858_e9cb257272_z.jpg


is equivalent to

{
...

...11011... ,
...10111... ,

...

}

By understanding the notion of common universe of different paths, one easily defines ...10011... as the non-overlapping result among ...11011... and ...10111... paths of the common unbounded binary tree.

Since the traditional mathematicians here are hard reductionists (the notion of unbounded binary tree as a common universe of different paths is beyond their scope) they reduce ...11011... and ...10111... into a single path.

Dear unbounded binary tree
don't be sad,
there are notions
that cherish your shade.
 
doronshadmi said:
Once again....
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Gibberish aside, what point do you think you are making? So far, you logic-defying conclusion has been that your codes is different from themselves. As doronetics concepts go, that one is superlatively useless.

You are still left with (a) you cannot tell your codes apart, and (b) you don't have enough of them even if you could.

Still stuck at step (3).
 
Let's help to the traditional mathematicians here.

(a) they cannot tell the codes apart (their difference w.r.t each other), and (b) they don't have enough of them because they are hard reductionists (in the case of ...10111 and ...11011... they are left with a single path, and then the blame others by their own failures).

As a result step (3) is not at their scope.
 
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doronshadmi said:
Let's help to the traditional mathematicians here.

(a) they cannot tell the codes apart, and (b) they don't have enough of them because they are hard reductionists (in the case of ...10111 and ...11011... they are left with a single path, and then the blame others by their own failures).

As a result step (3) is not at their scope.
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Well, perhaps you could tell us how you would decide whether two codes are different or the same.

Here's how I'd do it: Two codes are the same if and only if there exists an sequentially ordered mapping of the bits in one sequence to the bits of the other sequence in which bits are all pair-wise identical.

In other words, if I can align the two sequences so all the bits match, then they are identical. For my recurring example of ...110111... and ...111011..., I can align them on the solo 0 bits, so they are the same code.

Got anything like that?
 
doronshadmi said:
The clear answer is given in http://www.internationalskeptics.com/forums/showpost.php?p=8493921&postcount=1787 (after the Q.E.D), where one of the cases (...101... (self overlapping)) is the entire universe of the traditional mathematicians here.
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That would be the case where you declare (your favorite: proof by assertion) a code to be different from itself by application of a indeterminate method to yield an irrelevant result. Well done.

I will add this bit of fantastical nonsense to the list of truly stupid teachings of doronetics. It is on par with 2 is not a member of {2}.
 
One can align two sequences of "0;1" bits such that all the bits match, if the two sequences of "0;1" bits are not sequences of the same unbounded binary tree.

In that case the diversity of different sequences of "0;1" bits (as found if they are sequences of the same unbounded binary tree), is not considered.

Organic Mathematics considers this diversity (as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=8494232&postcount=1794), unlike the traditional approach of this fine subject.
 
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