Deeper than primes - Continuation

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doronshadmi said:
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.
Click to expand...


No, it doesn't, and no, you don't. You just inserted stuff that isn't there. All you have is a sequence of bits, infinitely long in both directions. The "unbounded binary tree" was yet another arbitrary addition you made that explains nothing, confuses you no end, and has no right being there in the first place.

Moreover, these "unbounded binary trees" of yours require you to select an align point. Select a different point of alignment, get a different tree. It's just another sloppy bit of self-confusion/self-delusion on your part through the addition of something completely unneeded.

Even your recently-improved theorem statement remains a monument to your self-confusion and self-delusion. You introduced a completely unnecessary second set. It does serve a purpose, though, I suppose. You can delude yourself into believing you can arbitrarily assign a new code for set U (which is also set X), conveniently ignoring that it was already assigned a code in step (3) because of the requirement stipulated in step (1).

Of course, that's where your first epic thread started, now, wasn't it? You took two complementary values (i.e. A and ~A), assigned them different names, then used them like independent values. And you wonder why we laugh at your "notions."

Your so-called proof is garbage. You reasoning is garbage. Your conclusions are garbage.
 
There is no way to be developed beyond hard reductionism if one does not able to comprehend the notion of a common universe (in that case an unbounded binary tree) of infinitely many sequences (of "0;1" bits, in the considered case).

Without the Tree/paths relations, the low sensitivity of hard reductionism rises its limited head.

For example, look at this phrase "Moreover, these "unbounded binary trees" of yours require you to select an align point. Select a different point of alignment, get a different tree."

1) We are talking about one and only one unbounded binary tree as a common universe of different infinitely many sequences of "0;1" bits along it, so the "Moreover, these "unbounded binary trees" of yours" simply misses this notion.

2) By saying "Select a different point of alignment, get a different tree." the traditional mathematician here is inconsistent with its own notions, because he agrees about different "unbounded binary trees", but he does not agree about different sequences along the same unbounded binary tree.

Now look at this phrase: "You can delude yourself into believing you can arbitrarily assign a new code for set U (which is also set X), conveniently ignoring that it was already assigned a code in step (3) because of the requirement stipulated in step (1)."

Here the traditional mathematician does not comprehend the inability to define the same code for set U and set X if set X is a member of set U.

This inability is exactly the result of http://www.internationalskeptics.com/forums/showpost.php?p=8493921&postcount=1787 proof (no matter what a given code and its complement are considered).
 
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Here is another phrase of the traditional mathematician here: "You took two complementary values (i.e. A and ~A), assigned them different names, then used them like independent values. And you wonder why we laugh at your "notions.""

In this case the traditional mathematician here can't comprehend that "two complementary values" are not less than mutually-independent (and not just independent) w.r.t each other, if they are opposites of a common universe.

Also ~A is not unconditionally the opposite of A (as wrongly understood by traditional mathematicians that uses excluded-middle).
 
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The following different branches ...101111..., ...110111..., ...111011..., ...111101..., etc. ad infinitum ... of the common unbounded binary tree, do not exist by the hard reductionism of the traditional mathematician here (only a single branch survives his reductionist reasoning):

7675724450_5006011159_z.jpg


Once again:

Dear unbounded binary tree
don't be sad,
there are notions
that cherish your shade.
 
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Doron,

You idiotic posts stand as a monument to your intellectual failings. I see no reason to comment on them further, and certainly not point by point since they are self-discrediting. I will, however, remind you that real Mathematics continues to work; your stuff, not so much.
 
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Dear unbounded binary tree
don't be sad,
there are notions
that cherish your shade.

In a barren desert
inside a dusty cave
some traditional notions
digging their own grave.
 
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Let's improve the notion of overlap among unbounded binary sequences as follows:

We check the matching between the bits of two unbounded binary sequences.

If there is a matching, than the result is 1, otherwise the result is 0.

for example:

Case A
...
1 _ 1 --> 1 |
1 _ 1 --> 1 |
0 _ 1 --> 0 |- no matching
1 _ 1 --> 1 |
1 _ 1 --> 1 |
...

Case B
....
1 _ 1 --> 1 |
1 _ 1 --> 1 |
0 _ 0 --> 1 |- matching
1 _ 1 --> 1 |
1 _ 1 --> 1 |
...

Case C
...
1 _ 1 --> 1 |
0 _ 1 --> 0 |
1 _ 1 --> 1 |- no matching
1 _ 0 --> 0 |
1 _ 1 --> 1 |
...

By translating it into the notion of the traditional mathematician here, we get:

"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."

As can be clearly seen, Case B(=matching) and Case C(= no matching) results are not identical.


Case D
...
1 _ 0 --> 0 |
0 _ 1 --> 0 |
1 _ 0 --> 0 |- no matching
0 _ 1 --> 0 |
1 _ 0 --> 0 |
...

Also Case D has "no matching" result.
 
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doronshadmi said:
Let's improve the notion of overlap among unbounded binary sequences....
Click to expand...

You know, Doron, you could have just said you'd align the two sequences in arbitrary ways then compare them bit-wise. Just sayin'.

Your inability to use words notwithstanding, though, you have made it clear that in doronetics no sequence other than all 0's or all 1's is equal to itself. Truly a colossal accomplishment.
 
The Traditional mathematicians here arbitrarily force what they call "bit-wise" on the fine (non-arbitrary) structure of the given unbounded binary tree (which is a form of an organism):

Code: 
                              ...                           
               [B]1                               0[/B]                 
              / [B]\                             /[/B] \                
             /   [B]\                           /[/B]   \               
            /     [B]\                         /[/B]     \              
           /       [B]\                       /[/B]       \             
          /         [B]\                     /[/B]         \            
         /           [B]\                   /[/B]           \           
        /             [B]\                 /[/B]             \          
       /               [B]\               /[/B]               \         
       1               [B]0               1[/B]               0         
      / \             [B]/[/B] \             / [B]\[/B]             / \        
     /   \           [B]/[/B]   \           /  [B] \[/B]           /   \       
    /     \         [B]/[/B]     \         /    [B] \[/B]         /     \      
   /       \       [B]/[/B]       \       /       [B]\[/B]       /       \     
   1       0       [B]1[/B]       0       1       [B]0[/B]       1       0     
  / \     / \     / [B]\[/B]     / \     / \     [B]/[/B] \     / \     / \    
 /   \   /   \   /   [B]\[/B]   /   \   /   \   [B]/[/B]   \   /   \   /   \   
 1   0   1   0   1   [B]0[/B]   1   0   1   0   [B]1[/B]   0   1   0   1   0   
/ \ / \ / \ / \ / \ [B]/[/B] \ / \ / \ / \ / \ / [B]\[/B] / \ / \ / \ / \ / \  
1 0 1 0 1 0 1 0 1 0 [B]1[/B] 0 1 0 1 0 1 0 1 0 1 [B]0[/B] 1 0 1 0 1 0 1 0 1 0  
                              ...

No wonder that the fine (non-arbitrary) structure of the given unbounded binary tree (as seen above) is destroyed, and we get
...
0 _ 0 --> 1 |
1 _ 1 --> 1 |
0 _ 0 --> 1 |- matching
1 _ 1 --> 1 |
0 _ 0 --> 1 |
...

or
...
1 _ 1 --> 1 |
0 _ 0 --> 1 |
1 _ 1 --> 1 |- matching
0 _ 0 --> 1 |
1 _ 1 --> 1 |
...

instead of

...
1 _ 0 --> 0 |
0 _ 1 --> 0 |
1 _ 0 --> 0 |- no matching
0 _ 1 --> 0 |
1 _ 0 --> 0 |
...

or

...
0 _ 1 --> 0 |
1 _ 0 --> 0 |
0 _ 1 --> 0 |- no matching
1 _ 0 --> 0 |
0 _ 1 --> 0 |
...


Actually the "You know, Doron, you could have just said ..." phrase fits to verbal_symbolic-only reasoning (this reasoning can't comprehend visual_spatial reasoning, exactly as visual_spatial-only reasoning can't comprehend verbal_symbolic reasoning).
 
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doronshadmi said:
Actually the "You know, Doron, you could have just said ..." phrase fits to verbal_symbolic-only reasoning (this reasoning can't comprehend visual_spatial reasoning, exactly as visual_spatial-only reasoning can't comprehend verbal_symbolic reasoning).
Click to expand...


In other news, today's phrase is receptive aphasia. Use it wisely.
 
The traditional mathematicians here have made it clear that in traditional mathematics sequences can't be compared also in vivo (also beyond reductionism). Truly a colossal accomplishment.

No wonder that by traditional mathematics' reasoning the whole is sum of parts.

For example, according to this reductionist reasoning the traditional mathematician here is a sum of parts, no matter if these parts appear as a living organism or a set of quantified chemical elements, which are closed in separate boxes.

Once again:

Mathematics for the majority of traditional mathematicians is no more than a mechanic (also called formal) game, where the mathematician's awareness is not a factor (does not have any influence on the, so called, platonic realm reports) of this game.

Such an attitude easily leads to non-responsibility that may characterizes the formal education of traditional mathematicians, especially the "pure" one (they claim that they deal with realms that are independent of the, so called, non-abstract realms).

Organic Mathematics' aim is to reduce the influence of this non-responsible mechanic formal education that was developed for the past 4000 years, and transform it into a framework that consistently enables to unify Ethical reasoning (in terms of evolutionary scale) AND Logical reasoning.

It can't be done, as long as the mathematical science in known as no more than a mechanic (also called formal) game, where the mathematician's awareness is not a factor (does not have any influence on the, so called, platonic realm reports) of this game (which is characterized by the built-in non-responsibility of its educational training, exactly because the trained mind learns how not to be a factor of this science, in order to develop his\her platonic realm reports).
 
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Let's research the following phrase:

"Your inability to use words notwithstanding, though, you have made it clear that in doronetics no sequence other than all 0's or all 1's is equal to itself. Truly a colossal accomplishment."

...11011... = ...10111... according to the one who wrote this phrase, but ...11011... is still too complex and by following the search after identity ...11011... is composed from simpler building-blocks, which are 0;1 bits.

So, if we wish to refine some identity, we actually have to choose the opposite way by define the relations of a given subject w.r.t a wider framework.

As a result, a given id is not less than Whole\parts relation, such that no amount of parts is the identity of the Whole.

Hard reductionists like the traditional mathematician here, can't comprehend that.
 
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doronshadmi said:
Let's research the following phrase:

"Your inability to use words notwithstanding, though, you have made it clear that in doronetics no sequence other than all 0's or all 1's is equal to itself. Truly a colossal accomplishment."

...11011... = ...10111... according to the one who wrote this phrase
Click to expand...

Hahaha doron, you can't even parse a simple sentence in English. Try again.
 
doronshadmi said:
The Traditional mathematicians here arbitrarily force what they call "bit-wise" on the fine (non-arbitrary) structure of the given unbounded binary tree (which is a form of an organism):

Code: 
                              ...                           
               [B]1                               0[/B]                 
              / [B]\                             /[/B] \                
             /   [B]\                           /[/B]   \               
            /     [B]\                         /[/B]     \              
           /       [B]\                       /[/B]       \             
          /         [B]\                     /[/B]         \            
         /           [B]\                   /[/B]           \           
        /             [B]\                 /[/B]             \          
       /               [B]\               /[/B]               \         
       1               [B]0               1[/B]               0         
      / \             [B]/[/B] \             / [B]\[/B]             / \        
     /   \           [B]/[/B]   \           /  [B] \[/B]           /   \       
    /     \         [B]/[/B]     \         /    [B] \[/B]         /     \      
   /       \       [B]/[/B]       \       /       [B]\[/B]       /       \     
   1       0       [B]1[/B]       0       1       [B]0[/B]       1       0     
  / \     / \     / [B]\[/B]     / \     / \     [B]/[/B] \     / \     / \    
 /   \   /   \   /   [B]\[/B]   /   \   /   \   [B]/[/B]   \   /   \   /   \   
 1   0   1   0   1   [B]0[/B]   1   0   1   0   [B]1[/B]   0   1   0   1   0   
/ \ / \ / \ / \ / \ [B]/[/B] \ / \ / \ / \ / \ / [B]\[/B] / \ / \ / \ / \ / \  
1 0 1 0 1 0 1 0 1 0 [B]1[/B] 0 1 0 1 0 1 0 1 0 1 [B]0[/B] 1 0 1 0 1 0 1 0 1 0  
                              ...

No wonder that the fine (non-arbitrary) structure of the given unbounded binary tree (as seen above) is destroyed, and we get [...]
Click to expand...

The "traditional" mathematician wouldn't fail to render a binary tree in such way that it would preserve the concept of branching through bifurcation (not to be confused with "bifornication" - an act that doesn't necessarily imply heterosexuality.) The nodes of a binary tree are usually arbitrarily defined

btree1.jpg


to accommodate the application of the binary tree in information theory. If a binary tree is considered a set, and it is usually the case, the nodes are the members of the set and therefore your definition of the nodes is embarrassingly incorrect. These are the branches of the tree that are defined with 1's and 0's, so that a particular path from the top of the tree to the bottom could be encoded, as shown below.

binary_tree_w_tags_class0.gif


Let's force gross mistakes on the "traditional" mathematician and show him the way out of his predicament with the help of doronetics and its universal, all-illuminating tree.
 
Let's compare between the following Binary trees:

Code: 
                              ...                           
               [B]1                               0[/B]                 
              / [B]\                             /[/B] \                
             /   [B]\                           /[/B]   \               
            /     [B]\                         /[/B]     \              
           /       [B]\                       /[/B]       \             
          /         [B]\                     /[/B]         \            
         /           [B]\                   /[/B]           \           
        /             [B]\                 /[/B]             \          
       /               [B]\               /[/B]               \         
       1               [B]0               1[/B]               0         
      / \             [B]/[/B] \             / [B]\[/B]             / \        
     /   \           [B]/[/B]   \           /  [B] \[/B]           /   \       
    /     \         [B]/[/B]     \         /    [B] \[/B]         /     \      
   /       \       [B]/[/B]       \       /       [B]\[/B]       /       \     
   1       0       [B]1[/B]       0       1       [B]0[/B]       1       0     
  / \     / \     / [B]\[/B]     / \     / \     [B]/[/B] \     / \     / \    
 /   \   /   \   /   [B]\[/B]   /   \   /   \   [B]/[/B]   \   /   \   /   \   
 1   0   1   0   1   [B]0[/B]   1   0   1   0   [B]1[/B]   0   1   0   1   0   
/ \ / \ / \ / \ / \ [B]/[/B] \ / \ / \ / \ / \ / [B]\[/B] / \ / \ / \ / \ / \  
1 0 1 0 1 0 1 0 1 0 [B]1[/B] 0 1 0 1 0 1 0 1 0 1 [B]0[/B] 1 0 1 0 1 0 1 0 1 0  
                              ...


binary_tree_w_tags_class0.gif


1) In both trees (if we assume an unbounded binary tree) cases like, for example

...
1 _ 1 --> 1 |
0 _ 1 --> 0 |
1 _ 1 --> 1 |- no matching
1 _ 0 --> 0 |
1 _ 1 --> 1 |
...

or

...
1 _ 0 --> 0 |
0 _ 1 --> 0 |
1 _ 0 --> 0 |- no matching
0 _ 1 --> 0 |
1 _ 0 --> 0 |
...

have no matching, whether nodes or branches are indexed by "0;1" bits.


2) In both trees no unique id of a given unbounded sequence of "0;1" bits is identical to the unique id of the tree as a whole (seen in http://www.internationalskeptics.com/forums/showpost.php?p=8493921&postcount=1787).


3) The second tree is a beautiful demonstration of how two "0;1" branches (which are at the level of parts) avoid contradiction at the "higher" level of their common node (which is at the level of the whole).
 
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The following diagram demonstrates 5 stages that reduce a given unbounded binary tree into some isolated sequence.

At each step we are losing the sequence's identity, which is derived from its relations with respect to other sequences as organs of the same tree:


7696889978_18236d26c7_k.jpg
 
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By not ignoring the finer identity that is derived form being sequences of the same unbounded binary tree, ...111... is the complement of the following sequences:

{
...,
...10111...,
...11011...,
...11101...,
...
}
 
By understanding identity in terms binary trees' levels, one enables to know that:

00.111... is not identical to 01.000...
01.111... is not identical to 10.000...
10.111... is not identical to 11.000...
...

etc. ... ad infinitum ... , as clearly shown by the following binary trees:

Code: 
        0                0                1                1             
        0                1                0                1             
        .                .                .                .             
       / \              / \              / \              / \            
      /   \            /   \            /   \            /   \           
     /     \          /     \          /     \          /     \          
    /       \        /       \        /       \        /       \         
    0       1        0       1        0       1        0       1     ... 
   / \     / \      / \     / \      / \     / \      / \     / \        
  /   \   /   \    /   \   /   \    /   \   /   \    /   \   /   \       
  0   1   0   1    0   1   0   1    0   1   0   1    0   1   0   1       
 / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \      
 0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1      
       ...              ...              ...              ...
 
doronshadmi said:
By understanding identity in terms binary trees' levels, one enables to know that:

00.111... is not identical to 01.000...
01.111... is not identical to 10.000...
10.111... is not identical to 11.000...
...
Click to expand...

Nobody has claimed otherwise. The binary sequences are definitely not identical. On the other hand, when interpreted as numbers expressed using a base-2 positional notation, the values are identical.

Thanks, doron, for providing an excellent example for when notational appearance doesn't resolve the simple question of meaning.
 
The traditional mathematicians here demonstrate their inability to interpret the following binary trees as numbers that are expressed by using a base-2 positional notation (see the "." that marks the border between fractions and integers).

The value of number 00.111... is not identical to the value of number 01.000...
The value of number 01.111... is not identical to the value of number 10.000...
The value of number 10.111... is not identical to the value of number 11.000...

etc. ... ad infinitum ... , as clearly shown by the following binary trees:



Code: 
        0                0                1                1             
        0                1                0                1             
        .                .                .                .             
       / \              / \              / \              / \            
      /   \            /   \            /   \            /   \           
     /     \          /     \          /     \          /     \          
    /       \        /       \        /       \        /       \         
    0       1        0       1        0       1        0       1     ... 
   / \     / \      / \     / \      / \     / \      / \     / \        
  /   \   /   \    /   \   /   \    /   \   /   \    /   \   /   \       
  0   1   0   1    0   1   0   1    0   1   0   1    0   1   0   1       
 / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \      
 0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1      
       ...              ...              ...              ...
 
doronshadmi said:
The traditional mathematicians here demonstrate their inability to interpret the following binary trees as numbers that are expressed by using a base-2 positional notation (see the "." that marks the border between fractions and integers).
Click to expand...


You buy straw wholesale, do you? You seem to have a lot.
 
What one enables to get if instead of using verbal_symbolic AND visual_spatial brain skills, one has straw instead of visual_spatial brain skills?


No wonder that such mind does its best in order to avoid sparks of new notions.
 
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doronshadmi said:
The traditional mathematicians here demonstrate their inability to interpret the following binary trees as numbers that are expressed by using a base-2 positional notation (see the "." that marks the border between fractions and integers).

The value of number 00.111... is not identical to the value of number 01.000...
The value of number 01.111... is not identical to the value of number 10.000...
The value of number 10.111... is not identical to the value of number 11.000...

etc. ... ad infinitum ... , as clearly shown by the following binary trees:



Code: 
        0                0                1                1             
        0                1                0                1             
        .                .                .                .             
       / \              / \              / \              / \            
      /   \            /   \            /   \            /   \           
     /     \          /     \          /     \          /     \          
    /       \        /       \        /       \        /       \         
    0       1        0       1        0       1        0       1     ... 
   / \     / \      / \     / \      / \     / \      / \     / \        
  /   \   /   \    /   \   /   \    /   \   /   \    /   \   /   \       
  0   1   0   1    0   1   0   1    0   1   0   1    0   1   0   1       
 / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \  / \ / \ / \ / \      
 0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1  0 1 0 1 0 1 0 1      
       ...              ...              ...              ...
Click to expand...

An Introduction to Applied Doronetics
 
The one who first made a link to the follow picture actually developed himself from Strawman into Logman (he is shy. if you look carefully you can see him standing on the log, in order to reinforce his applied result):

182783336_cd4dc59466.jpg
 
It is impossible to define a complete set of "0;1" sequences that are unbounded below, as clearly seen by Cantor's Diagonalization (without using any mapping between the members of two given sets):

Code: 
                               0
                               .
                              / \
                             /   \
                            /     \
                           /       \
                          /         \
                         /           \
                        /             \
                       /               \
                      /                 \
                     /                   \
                    /                     \
                   /                       \
                  /                         \
                 /                           \
                /                             \
               /                               \
               0                               1
              / \                             / \
             /   \                           /   \
            /     \                         /     \
           /       \                       /       \
          /         \                     /         \
         /           \                   /           \
        /             \                 /             \
       /               \               /               \
       0               1               0               1
      / \             / \             / \             / \
     /   \           /   \           /   \           /   \
    /     \         /     \         /     \         /     \
   /       \       /       \       /       \       /       \
   0       1       0       1       0       1       0       1
  / \     / \     / \     / \     / \     / \     / \     / \
 /   \   /   \   /   \   /   \   /   \   /   \   /   \   /   \
 0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

                              ...
 
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The traditional mathematicians here demonstrate their inability to interpret the following binary trees as numbers that are expressed by using a base-2 positional notation (see the "." that marks the border between fractions and integers).

The value of number 00.111... is not identical to the value of number 01.000...
The value of number 01.111... is not identical to the value of number 10.000...
The value of number 10.111... is not identical to the value of number 11.000...

etc. ... ad infinitum ... , as clearly shown by the following clearer binary trees:

Code: 
0               0               1               1                   
0               1               0               1      Integers     
.---------------.---------------.---------------.-----------------  
                                                       Fractions    
|\              |\              |\              |\                  
| \             | \             | \             | \                 
|  \            |  \            |  \            |  \                
|   \           |   \           |   \           |   \               
|    \          |    \          |    \          |    \          ... 
|     \         |     \         |     \         |     \             
|      \        |      \        |      \        |      \            
0       1       0       1       0       1       0       1           
|\      |\      |\      |\      |\      |\      |\      |\          
| \     | \     | \     | \     | \     | \     | \     | \         
|  \    |  \    |  \    |  \    |  \    |  \    |  \    |  \        
0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1       
|\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\      
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1     
                                                                    
                              ...

Since the birary trees are unbounded below, then no branch reaches any other branch "downward".
 
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Being unbound (at both sides, or not) means that the completeness of the Membership of the considered "0;1" unique sequences is not satisfied.


Code: 
 ...                        ...                                      
                                                                     
  |                            \                                     
  |                             \                                    
  |                              \                                   
  0                               1                                  
  |\                              |\                                 
  | \                             | \                                
  |  \                            |  \                               
  |   \                           |   \                              
  |    \                          |    \                             
  |     \                         |     \                            
  |      \           ...          |      \                           
  |       \                       |       \                          
  |        \                      |        \                         
  |         \                     |         \                        
  |          \                    |          \                       
  |           \                   |           \                      
  |            \                  |            \                     
  |             \                 |             \                    
  |              \                |              \                   
  0               1               0               1                  
  |\              |\              |\              |\                 
  | \             | \             | \             | \                
  |  \            |  \            |  \            |  \               
  |   \           |   \           |   \           |   \              
  |    \          |    \          |    \          |    \             
  |     \         |     \         |     \         |     \            
  |      \        |      \        |      \        |      \           
  0       1       0       1       0       1       0       1          
  |\      |\      |\      |\      |\      |\      |\      |\         
  | \     | \     | \     | \     | \     | \     | \     | \        
  |  \    |  \    |  \    |  \    |  \    |  \    |  \    |  \       
  0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1      
  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\     
  0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1    
                                                                     
                              ...                                    
                                                                     
                                                                     
  0               0               1               1                  
  0               1               0               1      Integers    
  .---------------.---------------.---------------.----------------- 
                                                         Fractions   
  |\              |\              |\              |\                 
  | \             | \             | \             | \                
  |  \            |  \            |  \            |  \               
  |   \           |   \           |   \           |   \              
  |    \          |    \          |    \          |    \          ...
  |     \         |     \         |     \         |     \            
  |      \        |      \        |      \        |      \           
  0       1       0       1       0       1       0       1          
  |\      |\      |\      |\      |\      |\      |\      |\         
  | \     | \     | \     | \     | \     | \     | \     | \        
  |  \    |  \    |  \    |  \    |  \    |  \    |  \    |  \       
  0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1      
  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\     
  0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1    
                                                                     
                                ...

By using also visual_spatial reasoning (in addition to verbal_symbolic reasoning) one easily knows the difference between local property (notated by "0" bits) and non-local property (notated by "1" bits) among the non-satisfied (in terms of infinite AND complete Membership) collection of sequences of "0;1" bits (whether they are understood as numbers, or not).
 
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doronshadmi said:
The value of number 00.111... is not identical to the value of number 01.000...
The value of number 01.111... is not identical to the value of number 10.000...
The value of number 10.111... is not identical to the value of number 11.000...

etc. ... ad infinitum ... , as clearly shown by the following binary trees:
Click to expand...

The value of a number is not determined by the notional representation of a number.

This will not change with a forest of posts.
 
cyborg said:
The value of a number is not determined by the notional representation of a number.

This will not change with a forest of posts.
Click to expand...
Mathematicians use different notations in order to determine the difference between the number itself (what you call "The value of a number") and some representation of it.

The number itself is represented by bold italic symbols, for example: 1.000...

Some representation (out of infinitely many possible representations) of 1.000... is 0.111...2

Since I distinguish between local and non-local properties of a given value (unlike "Traditional" Mathematics) is 0.111...2 is not some representation of 1.000..., or in other words, 0.111...2 is a non-local number < local number 1.000... by exactly non-local number 0.000...12

The distinction between local and non-local numbers is possible only if verbal_symbolic AND visual_spatial reasoning is used, exactly as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=8517019&postcount=1829.

You may ask: what is the meaning of "...1" expression in the non-local number 0.000...12?

My answer is: "...1" expression is the inability of the non-local number 0.111...2 to determine the exact value of the local number 1.000...

As can be seen in the following visual_spatial AND verbal_symbolic expression, the non-local number 0.111...2 and the local number 1.000... are in different levels of the considered mathematical space:

Code: 
0               0               1               1                   
0               [B]1[/B]               0               1      Integers     
[B].[/B]---------------[B].[/B]---------------.---------------.-----------------  
                                                       Fractions    
|[B]\[/B]              [B]|[/B]\              |\              |\                  
| [B]\[/B]             [B]|[/B] \             | \             | \                 
|  [B]\[/B]            [B]|[/B]  \            |  \            |  \                
|   [B]\[/B]           [B]|[/B]   \           |   \           |   \               
|    [B]\[/B]          [B]|[/B]    \          |    \          |    \          ... 
|     [B]\[/B]         [B]|[/B]     \         |     \         |     \             
|      [B]\[/B]        [B]|[/B]      \        |      \        |      \            
0       [B]1[/B]       [B]0[/B]       1       0       1       0       1           
|\      |[B]\[/B]      [B]|[/B]\      |\      |\      |\      |\      |\          
| \     | [B]\[/B]     [B]|[/B] \     | \     | \     | \     | \     | \         
|  \    |  [B]\[/B]    [B]|[/B]  \    |  \    |  \    |  \    |  \    |  \        
0   1   0   [B]1[/B]   [B]0[/B]   1   0   1   0   1   0   1   0   1   0   1       
|\  |\  |\  |[B]\[/B]  [B]|[/B]\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\  |\      
0 1 0 1 0 1 0 [B]1[/B] [B]0[/B] 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1     
                                                                    
                              ...
 
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doronshadmi said:
You may ask: what is the meaning of "...1" expression in the non-local number 0.000...12?.
Click to expand...

I might but I'd rather just ask you to define some functions that manipulate them - addition for example.

Until the symbols are shifted these are meaningless sequences.

Define your logic, construct a machine, turn the crank and see what pops out.

You may argue for a version of meaning where there are no meaningful differences - I find that inherently contradictory.

You may argue that the different number representations mean something different - but if under mathematical operation they behave no differently what difference does it make other than how one chooses to ink their page?

Do you know what it is you are arguing for?
 
doronshadmi said:
0.111...2 + 0.000...12 = 1.000...
Click to expand...

Don't forget to tell him how arithmetic in doronetics doesn't have those pesky commutative or associative properties that just get in the way. Then again, some of us are still waiting for you, Doron, to demonstrate how your imagined infinitesimal behaves differently than zero.

See? I can make bare assertions, too: 0.111...2 + 02 = 1.000...2. The only difference, though, between yours and mine is that mine works.
 
doronshadmi said:
0.111...2 + 0.000...12 = 1.000...
Click to expand...

I am not assuming any predefined existing notions of what 1, 0, 2, +, =, . may or may not mean in standard arithmetic.

First principles please otherwise these remain a bunch of meaningless symbols.
 
cyborg said:
I am not assuming any predefined existing notions of what 1, 0, 2, +, =, . may or may not mean in standard arithmetic.

First principles please otherwise these remain a bunch of meaningless symbols.
Click to expand...
Please assume 1, 0, 2, +, =,. , as used in standard arithmetic.

The new thing, in this case, is the non-locality of numbers as defined by using verbal_symbolic AND visual_spatial reasoning.

Please do not ignore http://www.scribd.com/doc/98276640/Umes if you wish to understand it.

Maybe http://www.scribd.com/doc/97823738/Unity-Awarness can be a better start.
 
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doronshadmi said:
Please assume 1, 0, 2, +, =,. , as used in standard arithmetic.
Click to expand...

I cannot - you are proposing something that does not fit into standard arithmetic.

You may be able to demonstrate that this is not the case and that they do reconcile but I would suggest that doing so from first principal would make the task easier to prove.

Otherwise I would no more assume that + means the same than I do when using it for boolean arithmetic or in writing code where the differences may be subtle and escape most but exist nonetheless.

The new thing, in this case, is the non-locality of numbers as defined by using verbal_symbolic AND visual_spatial reasoning.
Click to expand...

Show me what that means in formal logical terms. No amount of diagrams, pictures etc... will be more convincing to me than the cold logic of a Turning Machine clicking through its tape.
 
cyborg said:
I cannot - you are proposing something that does not fit into standard arithmetic.


You may be able to demonstrate that this is not the case and that they do reconcile but I would suggest that doing so from first principal would make the task easier to prove.

Otherwise I would no more assume that + means the same than I do when using it for boolean arithmetic or in writing code where the differences may be subtle and escape most but exist nonetheless.



Show me what that means in formal logical terms. No amount of diagrams, pictures etc... will be more convincing to me than the cold logic of a Turning Machine clicking through its tape.
Click to expand...

cyborg, my framework is irreducible into verbal_symbolic-only reasoning.

For the last time, please read the following articles:

http://www.scribd.com/doc/97823738/Unity-Awarness

http://www.scribd.com/doc/98276640/Umes

Deus ex machina is the researcher's self-awareness as inseparable factor of the results.
 
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