Deeper than primes

[doronshadmi]

That is not a result.

This is a result, which you evidently can't comprehend.

Now an evasion of http://www.internationalskeptics.com/forums/showpost.php?p=7297444&postcount=15758 was noted.

Before that an evasion of http://www.internationalskeptics.com/forums/showpost.php?p=7297036&postcount=15755 was noted, by ignoring a result that is based on expressions with non-local numbers.

 

[doronshadmi]

Aleph0 and Aleph1 are not the same as A and B defined by particular quantities. Imagine points as sub-atomic particles. Some astrophysicists see the origin of Big Bang in something called "Big Crunch," which is a scenario where all the matter in the pre-existing universe collapses under heavy gravitational influences into one point called "singularity." That means all the particles in the pre-existing universe were squeezed into a mass the size of our sun, for example. Then the contraction continued and the size of the ancestor universe was the one of the earth. That went on and the size shrank to such dimensions that the scientists must be given various awards to elevate their social image, otherwise folks would call them nuts: How can you squeeze all the matter in the universe into something smaller than a tennis ball?

So you can see a similarity between the same number of particles and the dimension of the objects that contain them, be it a sphere or your line segment:

the sun: __________________________________________________

the earth: ___________

the tennis ball: __

Since points are zero-dimensional, the "squeezing" goes much better and it's much safer as well, coz a line segment whose length approaches zero never explodes to become a very long line segment U_________E

You can't "squeeze" a collection of points (because a point is the smallest existing element) if they are totally cover a 1-dimensional element, so the different lengths of the line segments can't be explained by collections of points with the same cardinality.

In other words, you still do not understand the illogical traditional mathematical assertion about this profound subject, as can be found in http://www.internationalskeptics.com/forums/showpost.php?p=7297444&postcount=15758 and in the second part of http://www.internationalskeptics.com/forums/showpost.php?p=7296289&postcount=15750 .

 

[zooterkin]

This is a result, which you evidently can't comprehend.

Now an evasion of http://www.internationalskeptics.com/forums/showpost.php?p=7297444&postcount=15758 was noted.

Before that an evasion of http://www.internationalskeptics.com/forums/showpost.php?p=7297036&postcount=15755 was noted, by ignoring a result that is based on expressions with non-local numbers.

Why shouldn't nonsense be ignored? Your 'non-local numbers' are not a result. You have not properly defined them, nor have you shown what they are good for.

 

[epix]

You can't "squeeze" a collection of points (because a point is the smallest existing element) if they are totally cover a 1-dimensional element, so the different lengths of the line segments can't be explained by collections of points with the same cardinality.

In other words, you still do not understand the illogical traditional mathematical assertion about this profound subject, as can be found in http://www.internationalskeptics.com/forums/showpost.php?p=7297444&postcount=15758 and in the second part of http://www.internationalskeptics.com/forums/showpost.php?p=7296289&postcount=15750 .

You treat points as dimensional objects, like the particles in the universe that can be theoretically squeezed into an object smaller than a pea, otherwise you wouldn't raise that argument concerning identical cardinality and different length of line segments. You just don't understand the concepts that Cantor put forward. The main and incorrigible problem is that you misinterpret most of what the "traditional math" says.

 

[doronshadmi]

Why shouldn't nonsense be ignored? Your 'non-local numbers' are not a result.

Wrong.

They are the result of the inability of, for example, elements of lower dimensional space to completely cover higher dimensional space.

0.000...1[base 10] is a non-local number, which is a result of 1 - 0.999...[base 10]

You have not properly defined them,

They are well-defined under the co-existence of Non-locality and Locality, as can be seen by the following diagram:

nor have you shown what they are good for.

They are tools that are used to measure a non-entropic realm.

 

[doronshadmi]

You treat points as dimensional objects,

Points are the smallest EXITING elements, where each EXISTING point has exactly 0 dimensional space.

You do not distinguish between Nothing that does not exist and 0 that is an existing thing.

 

[doronshadmi]

otherwise you wouldn't raise that argument concerning identical cardinality and different length of line segments.

This is exactly the argument that shows the fallacy of the traditional mathematical assertion about the ability to completely cover a line by a set of the smallest elements (known as points), such that all these sets have the same amount of elements (points) even if the totally covered elements (lines) have different lengths.

You still have no clue about the fallacy of Cantor's reasoning on that profound subject. I call Cantor's reasoning about this subject "Death by Entropy" reasoning, and I am doing it for a very good reason, which is: The Cantorean reasoning is "Death by Entropy" of the human mind.

The main and incorrigible problem is that you misinterpret most of what the "traditional math" says.

Wrong.

I expose the "Death by Entropy" nature of Traditional Math on the human mind.

 

[zooterkin]

Wrong.

They are the result of the inability of, for example, elements of lower dimensional space to completely cover higher dimensional space.

And yet when asked you never managed to show anywhere on a line that a point cannot be found.

0.000...1[base 10] is a non-local number, which is a result of 1 - 0.999...[base 10]

You don't listen to anything you're told, do you? For a start the [base 10] is completely unnecessary, as has been mentioned before. Secondly, 1 - 0.999... is zero; again, as you've been told before.

They are tools that are used to measure a non-entropic realm.

Ok, show these measurements, then. What 'non-entropic realm' did you measure, and how big was it?

 

[epix]

This is exactly the argument that shows the fallacy of the traditional mathematical assertion about the ability to completely cover a line by a set of the smallest elements (known as points), such that all these sets have the same amount of elements (points) even if the totally covered elements (lines) have different lengths.

You still have no clue about the fallacy of Cantor's reasoning on that profound subject. I call Cantor's reasoning about this subject "Death by Entropy" reasoning, and I am doing it for a very good reason, which is: The Cantorean reasoning is "Death by Entropy" of the human mind.

There are two sets:

A = {2, 4, 6, 8, ... }
B = {1, 3, 5, 7, ... }

If you delete n elements from A and k*n elements from B, the cardinality of both sets is still the same - Aleph0. Now prove that it is not so and then someone maybe willing to listen to your line segment complaints. Since you've failed to follow the spaghetti triangles moving toward infinity, it's hard to expect that you offer anything else but your coined terminology, which lacks any substance, as the proof.

Btw, can OM solve the following two expressions?

a) 7 AND 5 = x

b) 193 - 172 = 21 . . . . ?

 

[The Man]

EDIT:

The Man I am not a participator of your "running after my own tail" closed game.

Doron by your own accounting that’s all you have been doing for some 20 odd years now. You can stop anytime your want to, (or can you?).

A = “(that has no predecessor) AND (that has no successor)”

B = “(that has no successor) AND (that has no predecessor)"

So once again specifically asserting “A” = “B”

Every reasonable person, but you, that sees a statement like:


“((A AND B) is different than (B AND A)) is ordered” immediately understands that this statement is about the ability to strictly distinguish between A and B inputs under different orders, where AND connective is used here as simultaneous existence of A;B strict inputs, which provides a strict result. The commutativity of AND connective has no impact on the fact that the result is strict, and the result is strict because A;B inputs are strict.

Doron anyone that can read immediately understands that you just set your “A” equal to your “B” above and that your assertion of “A AND B) is different than (B AND A)) is ordered” is simply false as well as self contradictory because “AND” is commutative. The question remains why don’t you understand it?

Also every reasonable person, but you, that sees a statement like:

“((A AND B) is the same as (B AND A)) is unordered” immediately understands that this statement is about the inability to strictly distinguish between A and B inputs under different orders (because A;B values are in superposition, which prevent their strict ids), where AND connective is used here as simultaneous existence of A;B non-strict inputs, which provides a non-strict result. The commutativity of AND connective has no impact on the fact that the result is non-strict, and the result is non-strict because A;B inputs are non-strict.

“The inability to strictly distinguish between A and B inputs under different orders”? Doron you made them the same statement because, since “AND” in commutative, changing the “(that has no successor)”, “(that has no predecessor)” ordering around the “AND connective” can not change the statement. Again it simply does not matter what your “A” , “B” variables represent or even if thay are distinguishable or not because ““((A AND B) is the same as (B AND A))” due to the commutative property of “AND” which again does not make anything “unordered” but simply means that such changes in ordering about the connective can not change the statement. Again the question remains why you simply can not or don’t want to understand this?

Let's take, for example, the 2-Uncertainty x 2-Redundancy Distinction-Tree:

(AB,AB) (AB,A)  (AB,B)  (AB)    (A,A)   (B,B)   (A,B)   (A)     (B)     ()

A * *   A * *   A * .   A * .   A * *   A . .   A * .   A * .   A . .   A . .
  | |     | |     | |     | |     | |     | |     | |     | |     | |     | |
B *_*   B *_.   B *_*   B *_.   B ._.   B *_*   B ._*   B ._.   B *_.   B ._.

(2,2) = (AB,AB)
(2,1) = (AB,A),(AB,B)
(2,0)=  (AB)
(1,1) = (A,A),(B,B),(A,B)
(1,0)=  (A),(B)
(0,0)=  ()

Any appearance of that tree is called Distinction State (DS), where any DS is under a structure called Frame (F), for example: (AB ,B ) is a DS that is under (2,1) F. The order in each DS or F has no significance (similar to {a,b}={b,a}) but any DS is the basis of any possible order (similar to the concept of Set as being the basis of permutations).

--------------------------

You will note no connectives in your “example” and your assertion that “The order in each DS or F has no significance” does not make them “unordered”. It just means that you have asserted that such changes in ordering “has no significance”.

Some example:

A = True
B = False

AB AND AB has non-strict result because the input is non-strict.

Again algebra deals with variables all the time, that you want to call your variable “AB” is irrelevant.

AB AND A or A AND AB has non-strict result because the input is non-strict (the commutativity of AND connective has no impact on the non-strict result).

The result of “AB AND A or A AND AB” is simply your “AB” variable as “A = True”

AB AND B or B AND AB has non-strict result because the input is non-strict (the commutativity of AND connective has no impact on the non-strict result).

Since “B = False” your “AB AND B or B AND AB” result is always “FALSE” and your “AB” variable simply can not change that result

A AND B or B AND A is strictly False (the commutativity of AND connective has no impact on the strict result).

Again since “B = False” your “A AND B or B AND A” result is always “FALSE”. Funny how you’re not talking about ordering now when that was the gist of your fallacious assertions involving the “AND connective” before.

--------------------------


The current use of AND connective inputs is limited only to DS (A,A),(B,B),(A,B) under F (1,1), and by this limitation we get only strict results, where the commutativity of AND connective has no impact on the strict property of the results.

Nope, again try your nonsense with a connective that is not commutative and see the “impact” of changes in ordering.

Organic Mathematics is not limited only to strict inputs, and without this limitation we get also non-strict results, where also in this case the commutativity of AND connective has no impact on the non-strict property of the results.

Mathematics isn’t “limited only to strict inputs”, again that’s why there are variables.

In other words The Man, your "running after my own tail" closed game, does not even scratch my arguments.

Doron you’ve been running after your own tail for decades and have yet to even scratch the surface of mathematics as evidenced by the fact that you apparently think that variables are something new.

Once again you evidently simply do not understand symmetrical and non-strict values (which are naturally unordered) exactly because your reasoning is limited only to DS (A,A),(B,B),(A,B) under F (1,1). You simply can't get anything beyond it.

Again you evidently don’t understand that claiming that a change in ordering “has no significance” doesn’t make anything “unordered” it just means that you are asserting that such a change in ordering “has no significance”.

-------------------------


Furthermore, you have asked about OM results, so one of OM results is the exposure of the limitations of your reasoning to DS (A,A),(B,B),(A,B) under F (1,1). You simply can't get anything beyond it and as a result you don't understand that the commutativity of AND connective has no impact on the result, whether it is strict or non-strict.

Nope you have simply exposed your lack of understanding of a variable. Now you might be claiming that your deliberate ignorance of such topics is a “result” of your “OM” but it would be equally demonstrable that your “OM” is simply the result of your deliberate ignorance of such topics.

Again try your nonsense with a connective that is not commutative and see the “impact on the result” with changes in ordering.

 

[doronshadmi]

Doron by your own accounting that’s all you have been doing for some 20 odd years now. You can stop anytime your want to, (or can you?).



So once again specifically asserting “A” = “B”




Doron anyone that can read immediately understands that you just set your “A” equal to your “B” above and that your assertion of “A AND B) is different than (B AND A)) is ordered” is simply false as well as self contradictory because “AND” is commutative. The question remains why don’t you understand it?



“The inability to strictly distinguish between A and B inputs under different orders”? Doron you made them the same statement because, since “AND” in commutative, changing the “(that has no successor)”, “(that has no predecessor)” ordering around the “AND connective” can not change the statement. Again it simply does not matter what your “A” , “B” variables represent or even if thay are distinguishable or not because ““((A AND B) is the same as (B AND A))” due to the commutative property of “AND” which again does not make anything “unordered” but simply means that such changes in ordering about the connective can not change the statement. Again the question remains why you simply can not or don’t want to understand this?

The Man you have totally failed to get http://www.internationalskeptics.com/forums/showpost.php?p=7294686&postcount=15740 exactly because your reasoning is stuck under the of the commutativity of AND connective, which clearly has no impact on the strict or non-strict output.

Once again, only the strict or non-strict input determines the strict or non-strict output.

You can release yourself from the irrelevancy of the commutativity of AND connective on strict or non-strict result at any time.

Until this moment it appears that you like very much to push your mind into dead end corners, by running after your own tail.

You will note no connectives in your “example” and your assertion that “The order in each DS or F has no significance” does not make them “unordered”. It just means that you have asserted that such changes in ordering “has no significance”.

It just means that you are unable the understand non-strict values like AB superposition.

Again algebra deals with variables all the time, that you want to call your variable “AB” is irrelevant.

"AB" is not some strict name of a variable.

"AB" is superposition of variables, which has no clear determination.

The result of “AB AND A or A AND AB” is simply your “AB” variable as “A = True”

Wrong.

The output of "AND A or A AND AB input" is indeterminate because AB input is indeterminate, and once again it is clearly seen that the commutativity of AND connective has no impact on the output.

Since “B = False” your “AB AND B or B AND AB” result is always “FALSE” and your “AB” variable simply can not change that result

Again since “B = False” your “A AND B or B AND A” result is always “FALSE”. Funny how you’re not talking about ordering now when that was the gist of your fallacious assertions involving the “AND connective” before.

The Man you take "AB" expression as "B AND A" or "A AND B" and totally miss the understanding that "AB" is the indistinguishably of A;B variables under superposition.

It is not funny that you can't comprehend "AB" expression as superposition.

Nope, again try your nonsense with a connective that is not commutative and see the “impact” of changes in ordering.

Again try your nonsense with a connective that is not commutative and see the “impact on the result” with changes in ordering.

Again, try to use inputs that are in superposition, in order to realize that the commutativity or the non-commutativity of the logical connective has no impact on strict or non-strict output.

Mathematics isn’t “limited only to strict inputs”, again that’s why there are variables.

Your failure to understand "AB" superposition input and its impact on the output (where the commutativity or non-commutativity of a given logical connective has no impact on strict or non-strict output), clearly demonstrates the limitation of traditional mathematics only to strict inputs, of the forms (A [logical connective] A), (B [logical connective] B), (A [logical connective] B), (B [logical connective] B), which are closed under F (1,1).

Doron you’ve been running after your own tail for decades and have yet to even scratch the surface of mathematics as evidenced by the fact that you apparently think that variables are something new.

The Man, you are unable to comprehend, for example, "AB" expression as a superposition of variables, and the impact of superposition on the result.

Again you evidently don’t understand that claiming that a change in ordering “has no significance” doesn’t make anything “unordered” it just means that you are asserting that such a change in ordering “has no significance”.

You still do not comprehend the simultaneity of superposition, which is naturally unordered, because there are no clear values under superposition, that their order may be considered as insignificant, or not.

Nope you have simply exposed your lack of understanding of a variable. Now you might be claiming that your deliberate ignorance of such topics is a “result” of your “OM” but it would be equally demonstrable that your “OM” is simply the result of your deliberate ignorance of such topics.

Nope you have simply exposed your lack of understanding of superposition of variables, where "AB" is an example of such superposition, and it is definitely not a name of some variable.

You can't get that exactly because your reasoning is closed under the particular case of F (1,1).

 

[epix]

Once again, only the strict or non-strict input determines the strict or non-strict output.

That can be visualized:

 

[doronshadmi]

And yet when asked you never managed to show anywhere on a line that a point cannot be found.

You are wrong, for every particular point along a given line, it is trivial to show some part of that line that is not covered by that particular point, etc... ad infinitum.

So I preferred the non-trivial way by comparing between the |R| magnitude and |1-dimensional| magnitude, which clearly shows that |R| < |1-dimensional| exactly because 1-dimensional elements have different lengths even is the cardinality of R members along them, is the same.

In other words, you don't understand http://www.internationalskeptics.com/forums/showpost.php?p=7297444&postcount=15758

You don't listen to anything you're told, do you? For a start the [base 10] is completely unnecessary, as has been mentioned before. Secondly, 1 - 0.999... is zero; again, as you've been told before.

You don't listen to anything you're told, do you?

For a start the [base 10] is completely necessary, as has been mentioned before (for example: 0.000...1[base 10] < 0.000...1[base 9]), but, as usual, you ignore it.

Ok, show these measurements, then. What 'non-entropic realm' did you measure, and how big was it?

I already did it in http://www.internationalskeptics.com/forums/showpost.php?p=7297036&postcount=15755 and http://www.internationalskeptics.com/forums/showpost.php?p=7299967&postcount=15765.

 

[doronshadmi]

There are two sets:

A = {2, 4, 6, 8, ... }
B = {1, 3, 5, 7, ... }

If you delete n elements from A and k*n elements from B, the cardinality of both sets is still the same - Aleph0. Now prove that it is not so and then someone maybe willing to listen to your line segment complaints.

It is totally irrelevant to my augments in http://www.internationalskeptics.com/forums/showpost.php?p=7299710&postcount=15762, which demonstrates your misunderstanding of them.

 

[zooterkin]

You are wrong, for every particular point along a given line, it is trivial to show some part of that line that is not covered by that particular point, etc... ad infinitum.

For a start the [base 10] is completely necessary, as has been mentioned before (for example: 0.000...1[base 10] < 0.000...1[base 9]), but, as usual, you ignore it.

Base 10 is assumed, unless otherwise specified. By your logic, you'd need to specify what base the '10' is in, so you'd never actually finish writing one single number...

0.000...1[base 10 [base 10[base 10[base 10[base10....]

I already did it in http://www.internationalskeptics.com/forums/showpost.php?p=7297036&postcount=15755 and http://www.internationalskeptics.com/forums/showpost.php?p=7299967&postcount=15765.

I see no measurement there. Try again.

 

[epix]

It is totally irrelevant to my augments in http://www.internationalskeptics.com/forums/showpost.php?p=7299710&postcount=15762, which demonstrates your misunderstanding of them.

It is relevant, but you have descended so deep to the well of chaos that you can grasp the relevancy. The proof that you absolutely have no idea about what is being said to you is your failure to solve the trivial equation 7 AND 5 = x.. You can only dress logical connectives into a weird outfit to make them dysfunctional for any logical purpose and the same goes for R: you asked the set for a mad dance and turned it into a zombie.

 

[doronshadmi]

It is relevant, but you have descended so deep to the well of chaos that you can grasp the relevancy.

epix, it is not relevant because by traditional mathematics a set of |N| points does not have the magnitude of the continuum, where only a set of |R| points has the magnitude of the continuum (where by traditional math, a set of points that has the magnitude of the continuum, completely covers a 1-dimensional element).

By using traditional mathematics climes about a set of points that (according to traditional mathematics) has the magnitude of the continuum, I clearly show that only a set of |R| points can't explain the differences of lengths among the following 1-dimensional elements:

Furthermore, by this diagram there are no proper subsets for R members exactly because they are results of common intersections, marked by the black lines.

The proof that you absolutely have no idea about what is being said to you is your failure to solve the trivial equation 7 AND 5 = x.. You can only dress logical connectives into a weird outfit to make them dysfunctional for any logical purpose and the same goes for R: you asked the set for a mad dance and turned it into a zombie.

Again, your "7 AND 5 = x" is a gibberish by traditional math, and this gibberish has nothing to do with traditional mathematics' claim that a set of |R| points has the magnitude of the continuum, such that it is completely covers 1-dimensional elements. You asked the set of |R| points and turned it into a traditional mathematics gibberish.

 

[doronshadmi]

Base 10 is assumed, unless otherwise specified.

Wrong. The base value must be written exactly because without it we do not know what 0.000...1 is considered.

By your logic, you'd need to specify what base the '10' is in, so you'd never actually finish writing one single number...

0.000...1[base 10 [base 10[base 10[base 10[base10....]

Wrong. This is not my logic, so we can learn from your reply that you do not understand my logic.

I see no measurement there. Try again.

0.000...1[base 10] = 1 - 0.999...[base 10] is a measured result that is based on using non-local numbers. Read it again, and this time do not put your gibberish on it.

 

[epix]

epix, it is not relevant because by traditional mathematics a set of |N| points does not have the magnitude of the continuum, where only a set of |R| points has the magnitude of the continuum (where by traditional math, a set of points that has the magnitude of the continuum, completely covers a 1-dimensional element).

It's not relevant to your phantasmagoric perception of sets, but the relevancy is apparent in the unmolested case. N is a subset of R, so the relevancy is generally granted. In turn, Z⁺ is also a subset of R. And so your idea that line (set R) cannot be completely "covered" by points also involves points in Z⁺. You've been asked several times to identify at least one positive integer which is not a subset of R, and you failed miserably and predictably to do so, mainly because you don't know how to formulate your conjectures so it would lead to a set of statements capable of forming a proof structure.

Again, your "7 AND 5 = x" is a gibberish by traditional math, and this gibberish has nothing to do with traditional mathematics' claim that a set of |R| points has the magnitude of the continuum, such that it is completely covers 1-dimensional elements. You asked the set of |R| points and turned it into a traditional mathematics gibberish.

You use 'AND' all the time to glue the broken pieces of the vase to hold the grey flowers of your disorganized, Ezekiel-like thoughts. That's why I didn't use the connective to relate variables P AND Q but actual values that would show that you don't know what to do when AND steps outside the usual application. If you take issues with "traditional" math, you should handle "not traditional" expressions.

If "7 AND 5 = x" is a "gibberish by traditional math," than there is no meaning to it and therefore there is no solution. So prove that there is no solution. Folks like you define the word "gibberish" as any collection of statements that they don't understand. But that's a fallacy. (See the Tower of Babel story.)

 

[zooterkin]

Wrong. The base value must be written exactly because without it we do not know what 0.000...1 is considered.

Why would it not be base 10?

Wrong. This is not my logic, so we can learn from your reply that you do not understand my logic.

I don't think there's any danger of you being accused of using logic.

0.000...1[base 10] = 1 - 0.999...[base 10] is a measured result that is based on using non-local numbers. Read it again, and this time do not put your gibberish on it.

It does not need any gibberish added, it has more than enough already.

Your 0.000...1 is an unnecessary and meaningless concept. Its value is the same as, well, the value of 1 - 0.999...