Deeper than primes

[sympathic]

EDIT:

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Again, Please pay attention that no bijection has been used here in order to prove the incompetence of the collection of real numbers.
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Bolding added.

 

[zooterkin]

No, OM shows that in order to get the exact area, one goes beyond the collection of points and gets the totally smooth curve, which is totally smooth exactly because it enables to be at AND not at (beyond) any given point (which is the property of non-locality).

It does? That's interesting. Can you share the details of exactly how it shows this (or anything else, for that matter)?

 

[doronshadmi]

It does? That's interesting. Can you share the details of exactly how it shows this (or anything else, for that matter)?

By the axiom of non-locality ( http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 )a curve is totally smooth only if it is at AND not at (beyond) the collection of points along it.

Also please look at http://www.internationalskeptics.com/forums/showpost.php?p=6696132&postcount=13509 and http://www.internationalskeptics.com/forums/showpost.php?p=6696147&postcount=1351 .

 

[doronshadmi]

Bolding added.

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is the best understanding of critical thinker like sympathic.

 

[jsfisher]

No, OM shows that in order to get the exact area, one goes beyond the collection of points and gets the totally smooth curve, which is totally smooth exactly because it enables to be at AND not at (beyond) any given point (which is the property of non-locality).

Make up your mind, please. On the one hand, first you say a curve was forbidden to have a point along it for it to bound an area. Now, you are willing to look beyond points. Perhaps at some time you'll come around to the notion of "continuous at all but a finite number of points."

On the other hand, you've abandoned "at the context of" in favor of simply "at". I would have guessed we are back to location and not domain or context, but you added the parenthetical "beyond" to the "not at" clause. Are you so deluded that you believe "beyond" is the antonym of "at"? Still, it is so nice to know that non-locality is such a powerful concept that you can so freely make continual changes to its meaning.

So, what does this latest round of nonsense tell us about Doronetics? Well, it tells us that where real Mathematics arrives at a result by simple and direct means under simple, defined conditions, Doronetics interposes meaningless and irrelevant every-changing considerations which it then looks "beyond," all the while borrowing the actual result from real Mathematics to claim as its own (without the need to do any real work).

In other words, Doron makes up stuff that is unnecessary nonsense and has no real bearing on the outcome. Moreover, since it is all nonsense, Doron continually adjusts it struggling to give the nonsense an appearance of significance.

 

[doronshadmi]

No Doron, you are the one who does not understand, as always. Aleph-0 is defined in terms of collections.

If one does not get the realm beyond collections, then he has no choice but to define its terms by using collections. This was the problem of Cantor in this case, and since you are following his steps, this is also your problem.

Nonsensical gibberish. A curve is a collection of ordered pairs (when in two dimensions). You are arguing with definitions again, like a fool.

Nonsensical gibberish. A curve is a non-local object that exists at and beyond any collection of points along it. You are closed under the concept of collections, like a fool.

No, you are the one using rational numbers in your set of irrationals, not me. Quit trying to rub off your blunders and failures onto others. If you want to give decimal expansions of irrationals, you have to make it clear that it does not terminate or repeat.

Utter nonsense, since I defined that set as the set of all irrational numbers, I do not have to mention the proprieties of numbers that are not irrational numbers.

Add the diagonal method to the list of elementary analysis concepts that you don't understand.

Add the diagonal method to the list of elementary concepts that you can't comprehend beyond your limited reasoning.

EDIT: To be more precise from my previous wording, the diagonal method can only be applied between a known countable set (the natural numbers) and an uncountable set to prove that there is no bijection from the countable set to the uncountable one. One set MUST be countable, because the diagonal method relies on the ability to make a list. You are trying to apply the diagonal method from an uncountable set to another uncountable one, which is complete nonsense.

More utter nonsense of a limited thinker. The diagonal method works perfectly among the members of one and only set even without using any bijection between the members of that set. By this really elementary use of the diagonal method we get exactly the same results of Godel's first incompleteness theorem, which demonstrates the validity of a thing according to the rules of a given framework that can't be proved within the given framework.

By using the diagonal method (without using any bijection) on the set of irrational numbers, we define an object that has the properties of that set (its obeys the rules of a give framework) but it is not a member of that set (but can't be proved within this framework).

The incompleteness the the set of irrational numbers is the simple and essential fact about this set, and this result is fully supported by Godel's first incompleteness theorem.

Cantor used a non-elementary use of his amazing diagonal method, by research the possibility of bijection between the natural numbers and real numbers.

Because of this non-elementary use he missed the elementary use of the diagonal method on the real numbers (where the elementary use is done without using any bijection).

If he was using the the elementary case of this amazing technique, he was able to understand that the need to add new numbers to a give set simply means that infinite collections are incomplete by definition, and no bijection checks can change this fundamental fact about infinite collections.

In other words HatRack, stay ignorant, put your head in your tiny and replicate Cantor's fundamental misunderstanding of the diagonal method.

 

[doronshadmi]

Make up your mind, please. On the one hand, first you say a curve was forbidden to have a point along it for it to bound an area.

No. The existence of a point along the curve does not change the fact that the curve exists even no point exists along it.

But in order to define the non-locality of that curve, we need to compare the curve's existence with the point(s) existence along it.

Once for all enter it into your mind: A definition of X is not X, exactly as (by analogy) "silence" is not silence.

A definition is wrongly used if it uses X in order to define X (and this mistake is shown at the ZF axiom of the empty set).

 

[jsfisher]

No. The existence of a point along the curve does not change the fact that the curve exists even no point exists along it.

You have left some important words out of that near sentence. Is this part of your master plan to prevent all communication?

But in order to define the non-locality of that curve, we need to compare the curve's existence with the point(s) existence along it.

Doron, thy name is Contradiction. Plus, the only one impressed with this non-locality nonsense is you. Since we are perfectly capable of producing valid results without your ill-defined gibberish, it has no relevance.

Once for all enter it into your mind: A definition of X is not X, exactly as (by analogy) "silence" is not silence.

Who has said otherwise? Well, except you, of course, in one of your fits of contradiction.

A definition is wrongly used if it uses X in order to define X (and this mistake is shown at the ZF axiom of the empty set).

No, that would be a comprehension gap of yours, not ours. The Axiom of Empty Set is not a definition for empty set. You really need to stop proclaiming things that are so monumentally incorrect.

 

[zooterkin]

It does? That's interesting. Can you share the details of exactly how it shows this (or anything else, for that matter)?

By the axiom of non-locality ( http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 )a curve is totally smooth only if it is at AND not at (beyond) the collection of points along it.

Also please look at http://www.internationalskeptics.com/forums/showpost.php?p=6696132&postcount=13509 and http://www.internationalskeptics.com/forums/showpost.php?p=6696147&postcount=1351 .

You could have saved yourself some typing, and just said, "No". Apart from being gibberish, what you've said doesn't say anything about the area.

Why don't you give an example of a curve, and show the working to get the area using OM?

 

[The Man]

and a value that can not go negative

-1 is a negative existing value, 1 is a positive existing value, 0 is non-negative and non-positive existing value.

No one of these exiting values is "that has to predecessor" (in the absolute sense), which is Emptiness.

So now your “magnitude of existence” can have a negative value?

Ah, I see ...

No, you don't.

Don’t what?

I certainly see that you still just like truncating quotes.

 

[epix]

No, OM shows that in order to get the exact area, one goes beyond the collection of points and gets the totally smooth curve, which is totally smooth exactly because it enables to be at AND not at (beyond) any given point (which is the property of non-locality).

If the Archimedes spiral area equals 1/3 of the circle's area, then the area must equal A = pi/3 for the circle with radius = 1. But does it?

Follow the rules of integration . . .

Yes, indeed. But there is that corollary that makes the result really precise only when the s-like symbol for integration ∫ is actually letter 'S', the first letter of "smooth." Would you believe that?

 

[dlorde]

Cybernetic kernels, Non-local Numbers, Emptiness, Fullness, Collection as an intermediate existence between Emptiness and Fullness, the non-locality of cross-contexts relations between context-dependent frameworks, the bridging between Ethics and Logic, mutations of already agreed terms, all these novel things (and more) are going to play a main role in the development of the Mathematical Science, and your context-dependent-only reasoning can't do anything in order to comprehend it.

So how about giving us a worked example, as hypothetical as you like, of OM realising its unique benefits in a way standard mathematics cannot ?

 

[HatRack]

There are so many absurdities and blunders in your reply it's impossible to respond to them all. So, let's focus on one:

By using the diagonal method (without using any bijection) on the set of irrational numbers, we define an object that has the properties of that set (its obeys the rules of a give framework) but it is not a member of that set (but can't be proved within this framework).

The diagonal argument is applied between the naturals and the reals as follows:

Suppose a correspondence between the naturals and the interval (0,1) can be established. Assuming any such correspondence:

1 0.R11 R12 R13 R14 R15...
2 0.R21 R22 R23 R24 R25...
3 0.R31 R32 R33 R34 R35...
...

Now, if Rnn ≠ 5, then let R0n = 5, and if Rnn = 5, then let R0n = 4. Thus, we have a real number R = 0.R01 R02 R03 R04 R05... in the interval (0,1) such that R is not in the list. Therefore, this interval must be uncountable, and the reals must also be uncountable. Since the rationals are countable, it follows that the irrationals are uncountable.

Of course, this argument relies on being able to list the natural numbers on the left, because otherwise there would be no way to index each number. In order to apply diagonalization to the irrationals as you claim to come up with another irrational not in such a set, you have to list the irrationals in a sequence, and use irrationals to index other irrationals.

So, let's see in details how all of the irrationals can be listed in a sequence so that diagonalization can be applied to them. Go ahead and try, it will be fun to watch considering it's been proven that you can't do so.

I see that it's been 7 long years and you still don't understand Cantor's Diagonal Argument. Here (http://www.physicsforums.com/showthread.php?t=10076), you foolishly tried to apply it to the rationals. It's funny how many cranks don't understand this basic argument that most undergraduate math majors can understand.

In other words HatRack, stay ignorant, put your head in your tiny and replicate Cantor's fundamental misunderstanding of the diagonal method.

Yes, I will get right back in my tiny of traditional mathematics, which has thousands of proven applications to the real world. Doronetics cannot even calculate the area under a curve.

 

[doronshadmi]

Of course, this argument relies on being able to list the natural numbers on the left, because otherwise there would be no way to index each number.

Utter nonsense. We do not need any index, because the considered numbers are unique and therefore distinct of each other.

Furthermore by using different bases, we can define 1 new distinct number by base 2 (0,1) diagonal number, 2 new distinct numbers by base 3 (0,1,2) diagonal number, 3 new distinct numbers by base 4 (0,1,2,3) diagonal number, etc ...

n=some arbitrary member of {1,2,3,4,5,...}

k= n+1

By generalization, we define n new distinct numbers for each base k diagonal number, and we clearly see the following fact:

1) The set of all irrational numbers does not exist.

2) Each base k set, has more members than base k-1 set.

EDIT:
By traditional mathematics these more members are taken as different representations of the same member, exactly because traditional mathematics takes the base value as some representation method (out of many other methods) of numerals.

 

[doronshadmi]

Yes, I will get right back in my tiny of traditional mathematics, which has thousands of proven applications to the real world. Doronetics cannot even calculate the area under a curve.

Again utter nonsense, thousands of proven applications, in this case, are based on forcing the incomplete convergent series to reach the non-locality of the curve, which is at AND not at (beyond) any convergent series, such that the incomplete convergent series does not have any influence on the precise result, where the precise result is achieved exactly because any non-local object is also not at (beyond) the convergent series.

So, let's see in details how all of the irrationals can be listed in a sequence so that diagonalization can be applied to them. Go ahead and try, it will be fun to watch considering it's been proven that you can't do so.

Suddenly, HatRack, you become a constructivist if it fits to your purpose, how refreshing

More utter nonsense. There is no restriction to represent a complete set of irrational numbers, exactly as there is no restriction to represent a complete set of natural numbers, or rational numbers.

We assume that, for example, that there is a complete set of irrational numbers, but by using the diagonal method we discover that this is a false assumption.

 

[epix]

2) Each base k set, has more members than base k-1 set.

Let me take a wild guess. Isn't that because k > k-1?

 

[doronshadmi]

So now your “magnitude of existence” can have a negative value?.

-1 is simply the existing mirror of +1.

 

[doronshadmi]

Let me take a wild guess. Isn't that because k > k-1?

It is because base k has more digits to play with and produce more new diagonal numbers than base k-1 case.

By traditional mathematics these more numbers are taken as different representations of the same number, exactly because traditional mathematics takes the base value as some representation method (out of many other methods) of numerals.

 

[HatRack]

Utter nonsense. We do not need any index, because the considered numbers are unique and therefore distinct of each other.

A diagonalization argument relies on the ability to create a list of something. Whenever you list a sequence of items in mathematics, you are implicitly using the natural numbers to index them. Hence, you're full of it.

 

[doronshadmi]

A diagonalization argument relies on the ability to create a list of something. Whenever you list a sequence of items in mathematics, you are implicitly using the natural numbers to index them. Hence, you're full of it.

HatRack, if you are non-constructivist you do not need any index to assume that there is a set of all infinitely many distinct irrational members.

By using the diagonal method it is proved that such a set is incomplete (the set of all irrational numbers does not exist).