Deeper than primes

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doronshadmi said:
In other words epix you are wrong because according to traditional mathematics |R| is a size (or magnitude) of collection of objects (0-dimensional elements, in this case), which is smaller than the size (or magnitude) of a 1-dimensional element, where Dimension is the property "of the same kind" that enables the comparison.
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Your claim lacks citation, which is a necessary addendum in your case, coz your interpretation of what the "traditional math" says is known to result in aggravated assault on the power set -- just to mentioned one instance where you completely lost your analytic footing.

You completely lack the necessary terminology to describe the relationships that you think exist. "Magnitude of real numbers" in connection with the size or cardinality of R simply doesn't exist in the traditional math terminology, yet you use the term to "repeat" what the traditional math says, which is a strong indicative of you not comprehending the story that the traditional math tells.

The cardinality of R and the cardinality of its subsets A and B as codomains is independent of the magnitude or length of line segments, as you can see below.

injectbiject.png


You just claim that rabbit can run faster than dormi completely oblivious to the fact that dormi doesn't exist.
 
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The Man said:
“A = True” was your own assertion Doron which means that “AB AND A or A AND AB” simply (and strictly) evaluates to “AB”
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A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.
 
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epix said:
Your claim lacks citation, which is a necessary addendum in your case, coz your interpretation of what the "traditional math" says is known to result in aggravated assault on the power set -- just to mentioned one instance where you completely lost your analytic footing.

You completely lack the necessary terminology to describe the relationships that you think exist. "Magnitude of real numbers" in connection with the size or cardinality of R simply doesn't exist in the traditional math terminology, yet you use the term to "repeat" what the traditional math says, which is a strong indicative of you not comprehending the story that the traditional math tells.

The cardinality of R and the cardinality of its subsets A and B as codomains is independent of the magnitude or length of line segments, as you can see below.

[qimg]http://img684.imageshack.us/img684/8067/injectbiject.png[/qimg]

You just claim that rabbit can run faster than dormi completely oblivious to the fact that dormi doesn't exist.
Click to expand...

Only your second diagram is relevant, and it is equivalent to the following diagram:

5876056051_22cd25ac8b_b.jpg


Sets A,B,C,D, ... etc. have the same cardinality (which is the size of a given set), which is |R| points and yet the size of the 1-dimensional elements is different exactly because |R| < |1-dimensional element| = the power of the continuum.

In other words, a set of |R| points does not have the power of the continuum, and one understands it only if he\she does not ignore the non-locality of 1-dimensional element under line\points co-existence (where a point is the minimal existing local element, and a line is the minimal existing non-local element, where no set of points has the property of non-local element).
 
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doronshadmi said:
A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.
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Very simple? Show a shade of mercy for Lord's wisdom, coz you took it to the heights only a few dare to climb:
The superposition calculus is a calculus for reasoning in equational first-order logic. It has been developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth-Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). As most first-order calculi, superposition tries to show the unsatisfiability of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation-complete — given unlimited resources and a fair derivation strategy, every unsatisfiable clause set can eventually be proved to be unsatisfiable.

As of 2007, most of the (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus.
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http://en.wikipedia.org/wiki/Superposition_calculus

Is the variable AB some union of mutually exclusive statements? Can you substitute AB with an example so the output given by the conjunction AND could be demonstrated by using an applicable example? I give you an example of the example:
The law of superposition (or the principle of superposition) is a key axiom based on observations of natural history that is a foundational principle of sedimentary stratigraphy and so of other geology dependent natural sciences:

“ Sedimentary layers are deposited in a time sequence, with the oldest on the bottom and the youngest on the top. ”

The law was formulated in the 17th century by the Danish scientist Nicolas Steno.
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http://en.wikipedia.org/wiki/Law_of_superposition

So like A=bottom and B=top. According to the pre-traditional logic, deposits accumulate from the bottom to the top. If AB = bottomtop, then according to
"AB AND A or AB AND A," which btw redefines the function of the coordinate conjunction "or", the output is non-strict. What is a non-strict output when you feed the beast with bottomtop AND bottom?


"No honey, don't spit the seed of the fruit, for nothing would spring in the organ we share with the squirrels."
Eve
 
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doronshadmi said:
Only your second diagram is relevant, and it is equivalent to the following diagram:

[qimg]http://farm7.static.flickr.com/6007/5876056051_22cd25ac8b_b.jpg[/qimg]

Sets A,B,C,D, ... etc. have the same cardinality (which is the size of a given set), which is |R| points and yet the size of the 1-dimensional elements is different exactly because |R| < |1-dimensional element| = the power of the continuum.

In other words, a set of |R| points does not have the power of the continuum, and one understands it only if he\she does not ignore the non-locality of 1-dimensional element under line\points co-existence (where a point is the minimal existing local element, and a line is the minimal existing non-local element, where no set of points has the property of non-local element).
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Your interpretation of "relevancy" doesn't allow you to make any basic comparison. What exactly is "the power of the continuum?" You just can't grasp the proof that the size of sets is independent of the magnitude and the position of the medium they are organized in. There is a bijection between

1234567 and 1 2 3 4 5 6 7

but ________ is shorter than _______________

If R doesn't have "the power of the continuum," then what does? Why don't you demonstrate the power of the continuum without using undefined, coined terms of yours?
 
epix said:
Your interpretation of "relevancy" doesn't allow you to make any basic comparison.
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Wrong epix. Your interpretation of "relevancy" doesn't allow you to make any basic comparison between the power of collection of local elements, and the power of the continuum, which is non-local.


epix said:
What exactly is "the power of the continuum?"
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The non-locality of the considered element.

epix said:
You just can't grasp the proof that the size of sets is independent of the magnitude and the position of the medium they are organized in.
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Wrong again epix.

The size of sets does not have the power of the continuum, simply because a collection of |R| objects of 0 size each is always less than the power of non-locality.

epix said:
There is a bijection between

1234567 and 1 2 3 4 5 6 7

but ________ is shorter than _______________
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Your example is irrelevant since your collection does not have |R| objects of 0 size each, along the line segments.

epix said:
If R doesn't have "the power of the continuum," then what does? Why don't you demonstrate the power of the continuum without using undefined, coined terms of yours?
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Why you are closed under the concept of collection, which its power is always less than the power of non-local element?
 
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epix said:
Very simple? Show a shade of mercy for Lord's wisdom, coz you took it to the heights only a few dare to climb:

http://en.wikipedia.org/wiki/Superposition_calculus

Is the variable AB some union of mutually exclusive statements? Can you substitute AB with an example so the output given by the conjunction AND could be demonstrated by using an applicable example? I give you an example of the example:

http://en.wikipedia.org/wiki/Law_of_superposition

So like A=bottom and B=top. According to the pre-traditional logic, deposits accumulate from the bottom to the top. If AB = bottomtop, then according to
"AB AND A or AB AND A," which btw redefines the function of the coordinate conjunction "or", the output is non-strict. What is a non-strict output when you feed the beast with bottomtop AND bottom?


"No honey, don't spit the seed of the fruit, for nothing would spring in the organ we share with the squirrels."
Eve
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By using your example, AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them. Because of this non-determination AB is not a contradiction.

Contradiction, in this case, is the result of forcing determination on the indeterminate.

AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.
 
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doronshadmi said:
AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.
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The major prophets who got the chance to contribute to the Bible with their visions were lucky that you were not born in antiquity. Yet, at the same time, you can't imagine what to substitute the variables A and B with. That makes you something like a false prophet and that's the other reason why there is no Book of Doron.

Suppose that A=false prophet and B=not false prophet, coz you've already made false/truth assignment to A and B. So what does your AB AND A --> A imply? I'm curious how your insight differs from the traditional view and treatment of the relationship between A and B:
For an equation describing a physical phenomenon, the superposition principle states that a combination of solutions to a linear equation is also a solution of it. When this is true the equation is said to obey the superposition principle. Thus if functions f1, f2 and f3 each solve the linear equation ψ, then ψ=c1f1+c2f2+c3f3 would also be a solution, in which each c is a coefficient. For example, the electrical field due to a distribution of charged particles can be described by the sum of the contributions of the individual particles.

Similarly, probability theory states that the probability of an event can be described by a combination of the probabilities of certain specific other events (see Mathematical treatment). For example, the probability of flipping two coins (coin A and coin B) and having at least one land head-up can be expressed as the sum of the probabilities for three specific events: coin A heads with B tails, coin A heads with B heads, and coin A tails with B heads. In this case the probability could be expressed as:

P(heads > = 1) = P(AnotB) + P(AandB) + P(BnotA)
or even:

P(heads > = 1) = 1 − P(notAnotB)
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(Note the commutativity of P(AnotB) and P(BnotA). Like if you commute from A to B and back from B to A going along the straight line, the distance travelled is the same.)

Coin tossing doesn't have to be parallel -- a sequential toss delivers head/tail result as well -- according to the "traditional math." Explain the difference in your parallel-only stipulation and don't forget to provide the example for the union of A and B, which is AB according to your prophecy... I mean a vision... I mean whatever it is.
 
doronshadmi said:
A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.
Click to expand...


Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.
 
doronshadmi said:
By using your example, AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them. Because of this non-determination AB is not a contradiction.

Contradiction, in this case, is the result of forcing determination on the indeterminate.

AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.
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So why not just call it what you claim it to be, ‘indeterminate’, as opposed to continuing calling it what you specifically claim it is not, a superposition? Unless your intent is simply to try to deliberately deceive? Perhaps it is because, as already noted before, being indeterminate is exactly what makes a variable, well, variable and in order for you to pretend that you’ve come up with something new you have to pretend your ‘indeterminate’ is something even you claim it is not, a superposition.
 
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The Man said:
Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.
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Do you find any justification to the above case where the grammatical conjuction "or" separates two identical clauses?

I initially set AB = 10 following Doron's assignment A=true=1 and B=false=0 and wound up with input

10 AND 0

There are tables that determine the "traditional" single-digit binary inputs, but I couldn't find any with multiple digit input. So I tried the alternative where the input is triangular,

1
...AND 0
0

to evaluate the relationship separately as

1 AND 0 --> 0
0 AND 0 --> 0

and that lineup returned 00=FalseFalse=BB.

What did you use to decode Doron's ciphergoulash to come up with AB?
 
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doronshadmi said:
Only your second diagram is relevant, and it is equivalent to the following diagram:

[qimg]http://farm7.static.flickr.com/6007/5876056051_22cd25ac8b_b.jpg[/qimg]
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The equivalency doesn't exist, only some similarity. Your diagram is not a convincing rendition. The length of the horizontal lines may be the same. See why.
 
epix said:
Do you find any justification to the above case where the grammatical conjuction "or" separates two identical clauses?
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Yes, because both of those clauses still evaluate the same.

epix said:
I initially set AB = 10 following Doron's assignment A=true=1 and B=false=0 and wound up with input

10 AND 0

There are tables that determine the "traditional" single-digit binary inputs, but I couldn't find any with multiple digit input. So I tried the alternative where the input is triangular,

1
...AND 0
0

to evaluate the relationship separately as

1 AND 0 --> 0
0 AND 0 --> 0

and that lineup returned 00=FalseFalse=BB.

What did you use to decode Doron's ciphergoulash to come up with AB?
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“AB”, as everything else is superfluous.

That’s the real rub of it epix, it doesn’t matter what Doron wants to call his variable, it is still a variable. That “A=TRUE” simply means that the result of any variable you “AND” with his “A” (in whatever order for those variables) is just going to be that variable (the “…AND A” or “A AND…” just becomes superfluous). Just as any variable you “AND” with “FALSE” (His “B”) is always going to result in “FALSE” (so the “AB AND…” or “…AND AB” just becomes superfluous).
 
The Man said:
Yes, because both of those clauses still evaluate the same.
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Are you saying that the or in Dorons, "Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output, was actually meant to be upper-case OR, the logical connective; and not lower-case or, the coordinating conjunction? I don't think there are too many people who would separate a single option by saying, Let's go to the movies or to the movies.
“AB”, as everything else is superfluous.

That’s the real rub of it epix, it doesn’t matter what Doron wants to call his variable, it is still a variable. That “A=TRUE” simply means that the result of any variable you “AND” with his “A” (in whatever order for those variables) is just going to be that variable (the “…AND A” or “A AND…” just becomes superfluous). Just as any variable you “AND” with “FALSE” (His “B”) is always going to result in “FALSE” (so the “AB AND…” or “…AND AB” just becomes superfluous).
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If the lower-case "or" is functional, then "AB AND A or AB AND A" results in two different inputs which are related by AND, like "movies or theater," for example. But what kind of clue is there to separate the case when the ANDed inputs are identical to each other?

AB AND A = movie
AB AND A = theater

I didn't go that far though and just tried to figure the output for AB AND A when A=True and B=False.
 
epix said:
The major prophets who got the chance to contribute to the Bible with their visions were lucky that you were not born in antiquity. Yet, at the same time, you can't imagine what to substitute the variables A and B with. That makes you something like a false prophet and that's the other reason why there is no Book of Doron.

Suppose that A=false prophet and B=not false prophet, coz you've already made false/truth assignment to A and B. So what does your AB AND A --> A imply? I'm curious how your insight differs from the traditional view and treatment of the relationship between A and B:


(Note the commutativity of P(AnotB) and P(BnotA). Like if you commute from A to B and back from B to A going along the straight line, the distance travelled is the same.)

Coin tossing doesn't have to be parallel -- a sequential toss delivers head/tail result as well -- according to the "traditional math." Explain the difference in your parallel-only stipulation and don't forget to provide the example for the union of A and B, which is AB according to your prophecy... I mean a vision... I mean whatever it is.
Click to expand...

Your reply has nothing to do with http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 .

You are still closed inside the traditional box, which can't comprehend mathematical objects line Uncertainty x Redundancy Distinction-Trees.
 
The Man said:
Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.
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Wrong The Man.

You simply refuse to deal with the fact that the commutativity of AND connective has no influence on the output, which is determined by the property of the input.

Since the input in the case of AB AND A or A AND AB is non-strict, so is the output.

Your limited reasoning can't comprehend, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807.

Your weak and limited reasoning is clearly seen by this kind of poor and limited reply:

The Man said:
doronshadmi said:
"AB" is not some strict name of a variable.
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You can call it whatever you want Doron, it changes nothing.
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The Man said:
doronshadmi said:
"AB" is superposition of variables, which has no clear determination.
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Sure it does it has the clear determination that it is not a superposition of anything. Since your “superposition” emphatically and by your own assertion does not involve the principle of superposition.
Click to expand...
 
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doronshadmi said:
Your reply has nothing to do with http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 .
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Your usage of "superposition" in your logical schemes got nothing to do with the meaning of the word.
You are still closed inside the traditional box, which can't comprehend mathematical objects line Uncertainty x Redundancy Distinction-Trees.
Click to expand...

Red und ancy ist inction?

You got redundant D in your statement -- a "superposition" of German, English and Gibberish.
 
epix said:
Your usage of "superposition" in your logical schemes got nothing to do with the meaning of the word.
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Wrong.

It adds parallel existence of the considered values that is resulted by non-determination, which becomes explicit by symmetry's break.

Take, for example, the 2-Uncertainty x 2-Redundancy Distinction-Tree:

Code: 
(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).
 
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doronshadmi said:
Wrong. They are equivalent.
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Lines which are parallel and lines which are not parallel are not equivalent. That's why God drew an arrow => below the exit sign so both fruity loops knew which way is out of Paradise.

= are parallel and mean "equals to"

> or < are not parallel and mean "greater than" or "less than"



Btw, Paradise or Garden of Eden are both mythical names. The place has been always called Fenway Park by the local fowl in the air.

||
||
||
W



Just learn the traffic symbols.
 
epix said:
Lines which are parallel and lines which are not parallel are not equivalent.
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It is equivalent if you compare between the sub-line segments of the red line segment and the green line segment.

They are smaller or bigger w.r.t each other in the same way as they are smaller or bigger w.r.t each other in my diagram.

In both cases, the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same.
 
epix said:
Lines which are parallel and lines which are not parallel are not equivalent.
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About being parallel, your blue lines and my blue lines are parallel w.r.t each other and also have different lengths w.r.t each other in both diagrams.

The green and red lines in your diagram are equivalent to some pair of black intersection lines in my diagram.

In other words, your second diagram and my diagram are equivalent.


Again, in both cases the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same along the different intersected line segments.

It has to be stressed that if Cardinality is the number of members of a given set that ignores their structure, then talking about Cardinality in terms of the power of the continuum is misleading, because the fundamental property of the continuum is defined by the non-locality given elements w.r.t other elements under locality\non-locality co-existence.

The first existing thing that has the power of the continuum is a 1-dimensional element, which exists simultaneously at least at two different existing locations, where these locations are first at least 0-dimensional elements, where no one of them or any number of them along the 1-dimensional element has the power of the continuum.

The power of the continuum = |1-dimensional element| > |R| = the number of all points along a line segment.

 
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doronshadmi said:
In both cases, the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same.
Click to expand...

doronshadmi said:
Again, in both cases the intersected line segments are smaller or bigger w.r.t each other, and no collection of |R| points along them provides the solution of these differences, exactly because according to traditional math, the power of |R| elements remains the same along the different intersected line segments.
Click to expand...


Saying basically the same wrong thing twice doesn't make it any less false.

Considering only finite cases often lead to incorrect inferences about the infinite, and that line segments may have different lengths doesn't contradict them being completely coverable by the same (infinite) number of points.
 
jsfisher said:
... , and that line segments may have different lengths doesn't contradict them being completely coverable by the same (infinite) number of points.
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Wrong jsfisher.

A collection of points can't have (the same cardinality) AND (the ability to completely cover 1-dimensional elements with different sizes).

A collection of |R| points does not have the power of the continuum, which is not less than |1-dimensional element|, and this is exactly the reason of why 1-dimensional elements have different sizes even if the number of all points along them is the same.

Jsfisher, your reasoning can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7318292&postcount=15803 .
 
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doronshadmi said:
Wrong jsfisher.

A collection of points can't have (the same cardinality) AND (the ability to completely cover 1-dimensional elements with different sizes).
Click to expand...

Other than your own disbelief, why not?

A collection of |R| points does not have the power of the continuum
Click to expand...

Perhaps you should look up the definition of "power of the continuum" before being so certain.

which is not less than |1-dimensional element|
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This phrase is nonsense. Dimensional elements don't have cardinality. Sets do.

and this is exactly the reason of why 1-dimensional elements have different sizes even if the number of all points along them is the same.
Click to expand...

Gibberish aside, this conclusion has no basis in logic.
 
doronshadmi said:
The power of the continuum = |1-dimensional element| > |R| = the number of all points along a line segment.
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"The power of continuum" is a very strange idea in the view of the simplicity of the "numerical" proof.

1) The length of line segment is a number x in R, such as x>0
2) Any x is divisible by y in R except zero.

There are two line segments m and n where m ≠ n. If you divide m and n by y, the result is a set of y-1 points drawn on the line segment plus 2 initial endpoints. Example: m = 12, n = 8, y = 4.

m: 12/4 = {0, 3, 6, 9, 12} = M
n: 8/4 = {0, 2, 4, 6, 8} = N

You see that |M| = |N|.

Since R = R, it follows that sets M = m/R and N = n/R must have the same cardinality, and so two line segments m and n of different length contain the same number of points.


Now the serpent was more crafty than any of the wild animals the LORD God had made. He said to the woman, “Did God really say, ‘You must not eat from any tree in the garden’?”
Genesis 3:1


1)SERpenT

or

2) SeRpEnT

:confused:

You must choose wisely. Use this prefetch: C stands for continuum and R is a set of real numbers. You must computate boldly the "cardinality" of line segment

C________R

to the unabridged joy of the little angels who will gladly blow their trumpets if you miss, so the fowl in the air would flap their wings to AC the world from The Heat of Defeat and other expellents.
 
jsfisher said:
Dimensional elements don't have cardinality. Sets do.
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Wrong.

The set of all points (where each point is 0-dimensional element) has cardinality |R| < |1-dimensional element| = the power of the continuum.

In other words, no set of points has the power of the continuum, exactly because each point is local w.r.t 1-dimensional element.

As long as your reasoning is limited to localities, it can't comprehend the power of the continuum, and this is exactly Cantor's failure of this profound and highly important subject (traditional Formalist and Platonist mathematicians are the followers of Cantor's failure of this profound and highly important subject, and you, jsfisher, simply one of them, no less, no more).

Generally (by not limited only to metric space) the power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.

Please look at the following analogy:

5721561558_c5b78c3152_b.jpg


Each given curvature is local w.r.t the 1-dimensional space, which is the common and non-local property of the collection of all these infinity many curvatures.

Only the 1-dimensional space exists at once at all these infinity many curvatures, which is a property that no given curvature has w.r.t 1-dimensional space.

By going beyond this analogy, no amount of localities has the property of non-locality, and only that has the property of non-locality has the power of the continuum.
 
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epix said:
"The power of continuum" is a very strange idea in the view of the simplicity of the "numerical" proof.
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The power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.
 
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The notion of Cardinality (in the traditional way), which actually ignores the structure of the considered members, is equivalent to the set of points, because no point has structure.

Yet |R| points do not have the power of the continuum, as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=7318292&postcount=15803.

Furthermore, by using Cardinality (in the traditional way) the power of the continuum of 1-dimensional element can't be defined,
because |{___}| = 1 by Cardinality traditional way.
 
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doronshadmi said:
Wrong.

The set of all points (where each point is 0-dimensional element) has cardinality |R| < |1-dimensional element| = the power of the continuum.
Click to expand...

Repeating your gibberish doesn't make it any less false. And stop trying to disprove definitions. It serves no real purpose other than to flaunt your confusion.
 
jsfisher said:
Repeating your gibberish doesn't make it any less false. And stop trying to disprove definitions. It serves no real purpose other than to flaunt your confusion.
Click to expand...
Staying in your limited box is resulted by getting what I say as gibberish.

For example your reasoning can't get the power of the continuum of _____ w.r.t to all |R| points along it, exactly because your reasoning can't comprehend the non-locality of _____ w.r.t the collection of |R| localities (points) along it.

I really do care about your limitations to get it, exactly because persons like you stand at the basis of our technological development, which is currently context-dependent-only technology, which has no cross-contexts reasoning of the technological results.

Without also cross-contexts reasoning of the results, context-dependent-only technology and disconnected reductionist-only specialization is going to fulfill itself by smashing its developers\ushers into pieces, because there is no common base ground that supplies the needed balance for the context-dependent aspect of the technological development.

The natural cross-contexts reasoning is exactly the non-subjective state of our awareness, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=7255966&postcount=15594 and http://www.internationalskeptics.com/forums/showpost.php?p=7241076&postcount=15569, which is resulted by new fundamental insights of the mathematical science ( for example: http://www.internationalskeptics.com/forums/showpost.php?p=7289466&postcount=15706 ) that can't be comprehended by context-dependent-only reasoning, which is currently the main stream of the mathematical science, which is stuck at the thinking process level that is the subjective-only level of one's awareness.
 
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doronshadmi said:
Staying in your limited box is resulted by getting what I say as gibberish.
Click to expand...

No, it is gibberish because you misuse words you simply do not understand. It does you no good to blame me for your own lack of knowledge.

Please stop trying to disprove definitions. It doesn't help you demonstrate anything approaching intelligence.
 
jsfisher said:
No, it is gibberish because you misuse words you simply do not understand. It does you no good to blame me for your own lack of knowledge.

Please stop trying to disprove definitions. It doesn't help you demonstrate anything approaching intelligence.
Click to expand...
jsfisher, you are blind to what is written in http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831.

I hope that soon minds like you, which are stuck at their thinking process level, will no longer be the majority.
 
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doronshadmi said:
jsfisher, you are blind to what is written in http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831.
Click to expand...

You continue to accuse others of your own failings. It is you who is blind to what you have written, your abuse of meaning, your abandonment of logic.

By the way, how is that example of some actual, tangible, significant result from this olio of gibberish you call OM coming along? Will you likely have anything soon, or is another 20+ years of wasted effort required?
 
jsfisher said:
You continue to accuse others of your own failings.
Click to expand...
jsfisher, we are all in the same boat, called planet Earth, so context-dependent only reasoning is definitely not the way for our survival on this planet.

Fortunately there are other voices in your community, which are aware of the impotence of cross-contexts reasoning development, in addition to context-dependent reasoning , as can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576 .

So I am optimistic about current and future development of the mathematical science, which is not going to be developed anymore by minds like you.
 
doronshadmi said:
jsfisher, we are all in the same boat, called planet Earth, so context-dependent only reasoning is definitely not the way for our survival on this planet.
Click to expand...

My, but you do inflate things, don't you? You also continue to reflect your failings onto others. They remain your failings.

Fortunately there are other voices in your community, which are aware of the impotence of cross-contexts reasoning development, in addition to context-dependent reasoning , as can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576 .
Click to expand...

I see you again misunderstand things others have written. The article you cite raised a point (30+ years ago, by the way) not completely unlike the point Hilbert raised over a century back. You misunderstood Hilbert, too. In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.

It in no way supports your gibberish, your confusion, your blatant denial of logic and reason, and certainly not the chaotic failure you call OM.
 
jsfisher said:
My, but you do inflate things, don't you? You also continue to reflect your failings onto others. They remain your failings.

I see you again misunderstand things others have written. The article you cite raised a point (30+ years ago, by the way) not completely unlike the point Hilbert raised over a century back. You misunderstood Hilbert, too. In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.

It in no way supports your gibberish, your confusion, your blatant denial of logic and reason, and certainly not the chaotic failure you call OM.
Click to expand...
A typical trivial reply of context-dependent-only mind, which can't get anything beyond his context-dependent-only reasoning.

Again, I am optimistic about current and future development of the mathematical science, which is not going to be developed anymore by minds like you, which can't get http://www.internationalskeptics.com/forums/showpost.php?p=7333688&postcount=15831 or http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576.
 
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jsfisher said:
In both cases, the point raised is reasonable and speaks to the overall beauty of Mathematics.
Click to expand...
Speaking about the overall beauty of Mathematics does not fulfill this beauty without actually using cross-contexts reasoning among context-dependent reasoning.

Your context-dependent-only reasoning missing it all along this thread.

For example, Cantor set elements are irreducible into disjoint points, simply because no 1-dimensional element is reducible to 0-dimensional element, so the assertion that Cantor set has Lebesgue measure 0 is false.
 
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doronshadmi said:
A typical trivial reply of context-dependent-only mind, which can't get anything beyond his context-dependent-only reasoning.
Click to expand...

Please, just stop, Doron. The failures are completely your own, not those of anyone else. You are not helping your cause by continually exposing your inabilities.
 
doronshadmi said:
The power of the continuum is the non-local property that gathers objects into a one form called collection.

No amount of objects has this power, exactly because any given gathered object is local w.r.t to the non-local property that has the power of the continuum.
Click to expand...

Your definition of "the power of the continuum" -- a substitute for |R| or aleph1 -- remains, like anything else you've come up with, unwrapped. How far do you think it gets when it encounters real enemy tanks?

Obviously, you don't get a bit of the essence of anything that is connected with "=". That's why you hate "traditional math," coz it supports it's statements with that particular symbol, and here is the evidence:

You are not aware of the fact that a set can divide a real number. Any math software returns a result to m/{a, b, c, d}, for example. Using some constants,

8/{1, 2, 3, 4} = {8, 4, 8/3, 2}.

That means m/A = B, where m is a real number and A and B are sets with the same size, or cardinality. When the dividing sets are finite, things are boring. The fun starts when the dividing set is the continuum, or set R.

m/R = ?

The expression on the left side divides m, which can be the length of a line segment, with the set of real numbers. R has a membership, but that cannot be put in 1 to 1 correspondence with the set of natural numbers. That's why the size of R is hypothetical aleph1 and not aleph0, which is the cardinality of the set of natural numbers and holds the set countably infinite. But that doesn't prevent you to indicate the intended . . .

m/R: m/{pi, √2, 9/8, e, Log(5), Sin(pi/7), ...}

If the cardinality of the denominator R is aleph1, then the result of the division must be set S which has the same cardinality as R, namely aleph1. It follows that

|m/R| = |n/R| where m≠n.

That means if m=2 and n=pi, for example, there is a 1 to 1 correspondence between all points on m and all points on n, which can be seen below through a consistent vertical mapping.


setsby.png



And that concludes the non-rigorous proof that the number of all points, which satisfy the definition of the real number and which are positioned alongside a 1-dim object, is independent of the magnitude of such an object.

Btw, how does OM find the magnitude of finite curves? Care to demonstrate the essence of the "power of the continuum?" How does OM figure the length of this object?


randclscurv.png
 
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