Deeper than primes

[jsfisher]

Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...)...

Stop right there. There are no "each values". A convergent infinite series (with the adjectives properly ordered) has one and only one value. Once again, doron shows he's total lack of understanding of the subject he's trying to discredit.

...is an accurate value, then the added result of infinitely many accurate values is itself an accurate value.

Actually, it does. A infinite series, if it converges, must of necessity converge to an accurate value.

A set of oranges is not itself an orange.

Exactly right, nor is an irrelevant analogy relevant.

 

[jsfisher]

L(K_n) is an invariant constant upon infinitely many scale levels, where the amount of the bends at each given scale level is finite. And this is exactly the reason of why X has an accurate value, no matter how infinitely many scale levels are involved.

Then why did you make the idiotic claim that X must be simultaneously greater than 0 and equal to 0?

“Approaches infinity” is a wrong notion simply because “approaches” is an essential property of any complex which is considered as infinite, and such a complex is resulted by an inaccurate value exactly because “approaches” is its essential property.

So, why didn't you just say you don't like limits, and you've left them out of doronetics? No need for all that gibberish and contorted logic.

Mind you, though, real Mathematics has no such trouble, so we'll keep using them, but you are free to handle such things in your dream world as you see fit. However, please stop trying to insist real math can't use them just because you don't understand them. They work consistently, without contradiction, so unless you can point out some new problem, we'll continue with them.

No, I clearly support my arguments all along the way, but you simply ignore them ( for example, now you ignore http://www.internationalskeptics.com/forums/showpost.php?p=5735873&postcount=9169) because your framework can’t deal with the real nature of inaccurate values.

Nope, there is no support there at all. You have completely failed to connect your insistence that X must equal 0 to anything mathematical. It has been just your standard say something sort of true, get totally confused, produce a bogus conclusion.

You made a bogus claim regarding real Mathematics. You cannot support the claim. Time to move on to the next topic you don't understand.

 

[doronshadmi]

No, of course not. You just said "the set of natural numbers" and stated that it is infinite. What is the difference between the "set of natural numbers" and the "set of ALL natural numbers"?

A very good question.

Aleph0 is an accurate (fixed) size that is greater than any positive whole number.

The size of N can be considered as the sum of all members of N, which is actually based on the long addition 1+1+1+..., such that each 1 of the long addition 1+1+1+... is related to each N member, without missing any N member.

But we know that 1+1+1+... has no accurate (fixed) size, so Aleph0 can’t be the sum of the long addition 1+1+1+..., even if each 1 of the long addition 1+1+1+... is related to each N member, without missing any N member.

Aleph0 is considered as an accurate (fixed) size by standard Math, where 1+1+1+... does not have an accurate (fixed) size by Standard Math (or in other words, it has no sum, where sum is an accurate value).

1+1+1+... is simply an inaccurate value < Aleph0, exactly because Aleph0 is greater than any positive whole number, and 1+1+1+... is related to these positive whole numbers , such that their inaccurate amount < Aleph0 accurate size.

In other words, 1+1+1+... is permanently an inaccurate size < Aleph0, and Aleph0 is permanently an accurate size > 1+1+1+... inaccurate size.

Conclusion: Aleph0 is an accurate (fixed) size that can’t be reached by infinitely many N members (their inaccurate size is permanently < Aleph0 accurate size) and as a result N is an incomplete mathematical object.

The incpmpleteness of any infinite collection is its inherent property.

 

[doronshadmi]

Stop right there. There are no "each values". A convergent infinite series (with the adjectives properly ordered) has one and only one value.

Exactly jsfisher, the convergent infinite series has an inaccurate value, which is a property that is different than any given part of that series.

Thank you for supporting OM’s reasoning.

Actually, it does. A infinite series, if it converges, must of necessity converge to an accurate value.

Exactly jsfisher.

An infinite series, if it converges, indeed permanently converges and therefore can’t reach the accurate value of the limit.

Thank you again jsfisher, by supporting OM’s reasoning.

Exactly right, nor is an irrelevant analogy relevant.

It is a very relevant analogy, jsfisher.

You simply unable to understand how it is related to this subject, because by your reasoning any given value must be accurate (fixed).

 

[doronshadmi]

Then why did you make the idiotic claim that X must be simultaneously greater than 0 and equal to 0?

Because by your idiotic reasoning the bended constant X > 0 must be also = 0 in order enable (2a+2b+2c+2d+...) to be X.

You simply can’t comprehend my proof without words on this subject.

So, why didn't you just say you don't like limits,

Like ??

I am talking here about a logical fact. Infinitely many added accurate values do not have an accurate value, because incompleteness is an inherent property of any infinite collection.

Mind you, though, real Mathematics has no such trouble,

Because what you call real Mathematics deals only with accurate (fixed) values.

Time to move on to the next topic you don't understand.

How typical jsfisher.

The word “understand” is to know what stands at the basis (under) of some reasoning.

Your reasoning deals only with fixed values, and as a result you can’t get the generalization (and reasoning) that deals with both accuracy and inaccuracy under a one comprehensive framework.

 

[sympathic]

A very good question.

Aleph0 is an accurate (fixed) size that is greater than any positive whole number.

The size of N can be considered as the sum of all members of N, which is actually based on the long addition 1+1+1+..., such that each 1 of the long addition 1+1+1+... is related to each N member, without missing any N member.

But we know that 1+1+1+... has no accurate (fixed) size, so Aleph0 can?t be the sum of the long addition 1+1+1+..., even if each 1 of the long addition 1+1+1+... is related to each N member, without missing any N member.

Aleph0 is considered as an accurate (fixed) size by standard Math, where 1+1+1+... does not have an accurate (fixed) size by Standard Math (or in other words, it has no sum, where sum is an accurate value).

1+1+1+... is simply an inaccurate value < Aleph0, exactly because Aleph0 is greater than any positive whole number, and 1+1+1+... is related to these positive whole numbers , such that their inaccurate amount < Aleph0 accurate size.

In other words, 1+1+1+... is permanently an inaccurate size < Aleph0, and Aleph0 is permanently an accurate size > 1+1+1+... inaccurate size.

Conclusion: Aleph0 is an accurate (fixed) size that can?t be reached by infinitely many N members (their inaccurate size is permanently < Aleph0 accurate size) and as a result N is an incomplete mathematical object.

The incpmpleteness of any infinite collection is its inherent property.

What a load of crap. But first thing's first: you have previously stated (that's putting it mildly...) N does not exist. Now you claim it does. Which one is it?

 

[jsfisher]

Exactly jsfisher, the convergent infinite series has an inaccurate value, which is a property that is different than any given part of that series.

Thank you for supporting OM’s reasoning.

Thank you for again demonstrating your failings in reading comprehension. You said it had many values; I said it didn't, that it has but one (accurate) value. You have quite the active imagination to believe I had supported your bizarre view of Mathematics.

Exactly jsfisher.

An infinite series, if it converges, indeed permanently converges and therefore can’t reach the accurate value of the limit.

Thank you again jsfisher, by supporting OM’s reasoning.

You are on a roll here for your own personal failures. Please don't attempt to pass on your gibberish as equivalent to what I wrote.

It is a very relevant analogy, jsfisher.

You simply unable to understand how it is related to this subject, because by your reasoning any given value must be accurate (fixed).

You keep saying things like this, but they are completely at odds with the facts. Keep trying though.

Maybe you'll eventually stumble across an actual inconsistency in Mathematics or perhaps something useful in doronetics.

 

[jsfisher]

Because by your idiotic reasoning the bended constant X > 0 must be also = 0 in order enable (2a+2b+2c+2d+...) to be X.

You repeat this idiotic claim, yet you cannot demonstrate it. Why is that?

 

[doronshadmi]

What a load of crap. But first thing's first: you have previously stated (that's putting it mildly...) N does not exist. Now you claim it does. Which one is it?

N is simply an incomplete collection of elements (its size is not fixed) that have a common given property.

1+1+1+... does not miss any member of N and still 1+1+1+... does not have a sum (a fixed size), where this inaccurate value < aleph0, which is a fixed size.

In other words, the real size of N is based on 1+1+1+... inaccurate value, where aleph0 is an accurate value > 1+1+1+... inaccurate value.

The real crap here is Cantor's wrong notion about the essential incompleteness of any infinite collection, because what Cantor did is to take the accurate size that can be found among finite sizes like 1, 1+1, 1+1+1, 1+1+1+1, … etc. and force it on 1+1+1+… naturally inaccurate size (again, please be aware that 1+1+1+… does not miss any N member and yet its size is inaccurate, such that 1+1+1+… < aleph0 accurate size).

Once again we see that what is called Standard Math is simply a framework that is tuned to deal only with fixed things.

In other words, it is a limited framework.

 

[doronshadmi]

Thank you for again demonstrating your failings in reading comprehension. You said it had many values; I said it didn't, that it has but one (accurate) value.

Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...)...

Stop right there. There are no "each values". A convergent infinite series (with the adjectives properly ordered) has one and only one value.

Exactly jsfisher, the convergent infinite series has an inaccurate value, which is a property that is different than any given part of that series.

Jsfisher, you can't understand OM exactly because you take only parts of what really has been written, and as a result you arrive to wrong conclusions about what really has been written, which is:

Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...) is an accurate value, then the added result of infinitely many accurate values is itself an accurate value.

Because of your intolerant behavior about what other people fully write, you have missed the simple notion, which clearly says that we cant conclude that the size of a given infinite series has an accurate value because each added size of that infinite series, has an accurate value.

Again, the set of oranges is not itself an orange (it is not similar to the property of its members).

The series of accurate values (2a+2b+2c+2d+...) does not itself have an accurate value.

This simple notion is beyond your limited reasoning, which deals only with accurate values.

You are on a roll here for your own personal failures.

You are on a roll here for a community of people, for the past 3,000 years, so?

Again the achievements of the mathematical science of the past 3,000 years are based only on dealing with accurate things.

As a result, the real nature of infinite collections is not understood by the framework that is used for the past 3,000 years.

A lot of useful results are based on fixed things, but it does not mean that the mathematical science must be closed under fixed things forever.

 

[sympathic]

N is simply an incomplete collection of elements (its size is not fixed) that have a common given property.

1+1+1+... does not miss any member of N and still 1+1+1+... does not have a sum (a fixed size), where this inaccurate value < aleph0, which is a fixed size.

In other words, the real size of N is based on 1+1+1+... inaccurate value, where aleph0 is an accurate value > 1+1+1+... inaccurate value.

The real crap here is Cantor's wrong notion about the essential incompleteness of any infinite collection, because what Cantor did is to take the accurate size that can be found among finite sizes like 1, 1+1, 1+1+1, 1+1+1+1, … etc. and force it on 1+1+1+… naturally inaccurate size (again, please be aware that 1+1+1+… does not miss any N member and yet its size is inaccurate, such that 1+1+1+… < aleph0 accurate size).

Once again we see that what is called Standard Math is simply a framework that is tuned to deal only with fixed things.

In other words, it is a limited framework.

Strange, I thought you did not believe in limits.

 

[sympathic]

Because of your intolerant behavior about what other people fully write,

project much?

 

[jsfisher]

Jsfisher, you can't understand OM exactly because you take only parts of what really has been written, and as a result you arrive to wrong conclusions about what really has been written

No, it is much simpler than that. Doronetics is incomprehensible because it is nonsense--contradictory, inconsistent, illogical, gibberish. You have yet to define anything that is a component part of doronetics, you have yet to provide any sort of credible refutation of the mathematics you do not understand but so desperately want to supplant, and you have yet to provide any example of "value" to your contradictory, inconsistent, illogical approach.

That's why your nonsense is rejected.

 

[doronshadmi]

No, it is much simpler than that. Doronetics is incomprehensible because it is nonsense--contradictory, inconsistent, illogical, gibberish. You have yet to define anything that is a component part of doronetics, you have yet to provide any sort of credible refutation of the mathematics you do not understand but so desperately want to supplant, and you have yet to provide any example of "value" to your contradictory, inconsistent, illogical approach.

That's why your nonsense is rejected.

jsfisher, your last post is not different than any chip propaganda of some dogmatic religious sect.

Please try to avoid this non-fruitful level.

Look how you (again) ignore the rest of one's post (http://www.internationalskeptics.com/forums/showpost.php?p=5753814&postcount=9190).

 

[doronshadmi]

Strange, I thought you did not believe in limits.

Again this impropriate word ("believe") about this fine and important subject (http://www.internationalskeptics.com/forums/showpost.php?p=5735963&postcount=9170)?

Sympathic, this subject has nothing to do with beliefs.

This subject is based on direct perception of the re-reached subject, which enables one to under-sand its fundamentals.

What you call Limit is simply a reflection the natural ability of our mind to look beyond some considered subject.

By looking beyond the considered subject (and in this case the considered subject can be infinite convergent series like 0+1/2+1/4+1/8+…, or a divergent series like 1+1+1+…) one must not ignore the fundamental fact that the used viewpoint of the considered subject is exactly beyond (greater or smaller than) the considered subject.

When this fundamental notion is used, one immediately understands that the considered subject can't have any value, which is beyond it.

This is exactly the case with an infinite divergent series like 1+1+1+…, it does not reach the value of the limit, known as aleph0.

Also, this is exactly the case with an infinite divergent series like 0+1/2+1/4+1/8+…, it does not reach the value of the limit, known as 1.

 

[doronshadmi]

Because by your idiotic reasoning the bended constant X > 0 must be also = 0 in order enable (2a+2b+2c+2d+...) to be X.

You repeat this idiotic claim, yet you cannot demonstrate it. Why is that?

Let us carefully research who's claim is right, on this case.

Here is the considered diagram:

By understanding this diagram, the following facts are shown (EDITED):

Fact 1) Constant accurate bended X size (the orange bended element) and convergent accurate Y sizes (the green elements) have common edges upon infinitely many scale levels.

Fact 2) Each accurate Y size is the complement of each accurate size of the infinite convergent series (2a+2b+2c+2d+…), to the accurate constant X size.

Fact 3) (2a+2b+2c+2d+…) = X only if Y=0, but if Y=0 then also X=0 because of fact (1).

Fact 4) If (2a+2b+2c+2d+…) = X, then X > AND = 0, because of fact (3).

Conclusion:

a) OM's claim ((2a+2b+2c+2d+…) < X) is right (X or Y are only > 0).

b) Standard Math's claim ((2a+2b+2c+2d+…) = X) is wrong ((X or Y are both > AND = 0).

 

[The Man]

No The Man.

I am talking about an accurate X value that is found upon infinitely many scale levels, where each level has a finite amount of bends.

I show that there is a 1-1 correspondence between any scale level of the constant and accurate X value, and any one of the accurate values of the infinite convergent series (2a+2b+2c+2d+...).

Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...) is an accurate value, then the added result of infinitely many accurate values is itself an accurate value.

A set of oranges is not itself an orange.

So now your “X” is not “an accurate value, called a sum” “upon infinitely many scale levels”? Did you lose your “X” at some “scale level” requiring it to be “found” again? You do understand that a claim “of the constant and accurate X value” requires that value to be both, well, “constant and accurate”, don’t you?

Again, rounded values are accurate values and also ranges of values that (by your own words) have sums, can’t be but accurate values.

Inaccurate values are not defined as some accurate values that do not reach another given accurate value (called, a limit by you).

An Inaccurate value is defined as permanently approaches value that can’t reach (can’t be) any given accurate value, whether the accurate value is called Limit, or not.

Well as usual you have your own definition (if you could call it that) of “accurate” which is inconsistent with the general definition as well as self-inconsistent. You do understand that the term value is singular, don’t you? A variable can approach some value of a limit, but that variable is a not singular value. It represents a range of values (that’s why it is called a variable because it varies in, well, value) that may or may not include some limit.

 

[doronshadmi]

So now your “X” is not “an accurate value

Please show where exactly X is not and accurate value, according to my post (you still do not get http://www.internationalskeptics.com/forums/showpost.php?p=5757263&postcount=9196).

A variable can approach some value of a limit, but that variable is a not singular value. It represents a range of values (that’s why it is called a variable because it varies in, well, value) that may or may not include some limit.

Exactly The Man.

In the case of Y=(2a+2b+2c+2d+...), Y is an inaccurate value, as long as Y is an infinite convergent series.

 

[The Man]

Let us carefully research who's claim is right, on this case.

Here is the considered diagram:

[qimg]http://farm3.static.flickr.com/2794/4464201033_30e7dbd8d4_o.jpg[/qimg]

By understanding this diagram, the following facts are shown:

Fact 1) Constant accurate bended X size (the orange bended element) and convergent accurate Y sizes (the green elements) have common edges upon infinitely many scale levels.

Fact 2) (2a+2b+2c+2d+…) = X only if Y=0, but if Y=0 then also X=0 because of fact (1).

Fact 3) If (2a+2b+2c+2d+…) = X, then X > AND = 0, because of fact (2).

Conclusion:

a) OM's claim ((2a+2b+2c+2d+…) < X) is right (X or Y are only > 0).

b) Standard Math's claim ((2a+2b+2c+2d+…) = X) is wrong ((X or Y are both > AND = 0).

Nope just your usual inconsistency. Your conclusion “2” (because it is only your conclusion not a fact) does not follow from your statement “1”. That your “X” and “Y” have the same “edges” (or end points) does not require them to have the same “size” as your conclusion “2” would require. In fact it is demonstrable from the first iteration of your series that your “X” and “Y” do not have the same “size” even though they have the same “edges” (or end point). So your conclusion “2” is proven false with the very first iteration of your series.

 

[doronshadmi]

Nope just your usual inconsistency. Your conclusion “2” (because it is only your conclusion not a fact) does not follow from your statement “1”. That your “X” and “Y” have the same “edges” (or end points) does not require them to have the same “size” as your conclusion “2” would require. In fact it is demonstrable from the first iteration of your series that your “X” and “Y” do not have the same “size” even though they have the same “edges” (or end point). So your conclusion “2” is proven false with the very first iteration of your series.

Here is a special longer version for you The Man, since you simply do not get the shroter version:

Fact 1) Constant accurate bended X size (the orange bended element) and convergent accurate Y sizes (the green elements) have common edges upon infinitely many scale levels.

Fact 2) Each accurate Y size is the complement of each accurate size of the infinite convergent series (2a+2b+2c+2d+…), to the accurate constant X size.

Fact 3) (2a+2b+2c+2d+…) = X only if Y=0, but if Y=0 then also X=0 because of fact (1).

Fact 4) If (2a+2b+2c+2d+…) = X, then X > AND = 0, because of fact (3).

Conclusion:

a) OM's claim ((2a+2b+2c+2d+…) < X) is right (X or Y are only > 0).

b) Standard Math's claim ((2a+2b+2c+2d+…) = X) is wrong ((X or Y are both > AND = 0).

EDIT:

Please look again at the edited version of http://www.internationalskeptics.com/forums/showpost.php?p=5757263&postcount=9196.