Deeper than primes

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jsfisher said:
Here, for example, the challenge was for you to show that X is 0 in the limit.
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No jsfisher, now you demonstrate that you have no clue what challenge has to be used in order to understand the considered subject.

The real challenge here is to show that X – (2a+2b+2c+2d+...) = 0

I proved that X – (2a+2b+2c+2d+...) > 0 exactly because X is a constant length upon infinitely many scale levels, and since (2a+2b+2c+2d+...) is found as long as constant X length is found, then since X can’t be length 0, then (2a+2b+2c+2d+...) < X, exactly because X can’t be length 0.

jsfisher said:
You babble instead about the relationship between X and a convergent series.
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In other words, you do not understand http://www.internationalskeptics.com/forums/showpost.php?p=5725971&postcount=9152 proof,
where X is a constant and accurate length > 0 upon infinitely many scale levels, and (2a+2b+2c+2d+..) definitely converges upon infinitely many scale levels.

jsfisher said:
you admit the series is convergent, but will separately argue the series doesn't converge.
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No jsfisher, (2a+2b+2c+2d+..) definitely converges (each arbitrary given segment is smaller than any arbitrary previous segment, upon infinitely many scale levels) exactly because constant X accurate length > 0 is found upon infinitely many scale levels.

Here is this beauty, that your limited Limit-oriented reasoning simply can’t comprehend:

4430320710_daf5b36c0f_o.jpg
 
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doronshadmi said:
Not once and not again, you have no argument The Man.

When you have something else to say, I am all ears.
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It is you once again you Doron that has no argument.

doronshadmi said:
Once again, X is a constant and accurate length > 0 in http://www.internationalskeptics.com/forums/showpost.php?p=5725971&postcount=9152 proof, that is not changed upon infinitely many scale levels.
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By claiming the segments of “X” have “no sum” “upon infinitely many scale levels” your are indeed claiming it has change and is no longer “a constant”.
 
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doronshadmi said:
If we deal with an infinite convergent series, then exactly because of the inseparable linkage between constant X AND (2a+2b+2c+2d+...) convergent series, X-(2a+2b+2c+2d+...) > 0, and as a result (2a+2b+2c+2d+...) < X.
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I see your reading comprehension problem continues.

In an earlier post, you said you had rigorously shown (your words, not those of anyone else) that "by standard mathematics" that X > 0 and X = 0, which would be a contradiction. What you said is being challenged.

Not that you showed it, rigorously or otherwise, I will agree that X > 0 at all steps in your construction. However, I do not agree X = 0, ever, neither at any step nor in the limit; I do not agree "by standard mathematics" X = 0; nor did you ever show that it was, rigorously or otherwise.

Please, stop with these irrelevant asides about the difference between X and some infinite series. Your incorrect and ridiculous insistence that you've shown X must be > 0 and = 0 at the same time ("by standard mathematics") is what is being challenged right now. Please focus.

Please support your bogus claim that X must be 0.
 
doronshadmi said:
No jsfisher, now you demonstrate that you have no clue what challenge has to be used in order to understand the considered subject.

The real challenge here is to show that X – (2a+2b+2c+2d+...) = 0
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The facts, is per usual, don't agree with you. In an earlier post you said:

doronshadmi said:
Limit is valid only if it can be reached, and it can be reached only by finitely many steps.

Force your obsolete reasoning about Limits and X > AND = 0, which is false.

Simple as that, and you can't do anything about this fact.
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Note the emphasized part. You said that. Either retract it as yet another bogus doronism where you again demonstrate your dearth of mathematical knowledge, or support the statement with yet another bogus doronism where you again demonstrate your dearth of mathematical knowledge.

Like it or not, nothing with limits in mathematics gets to the conclusion X both is > 0 and = 0. In your construction, X is always > 0, even in the limit.
 
The Man said:
By claiming the segments of “X” have “no sum” “upon infinitely many scale levels” your are indeed claiming it has change and is no longer “a constant”.
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No The Man.

X is an accurate value, called a sum.

(2a+2b+2c+2d+...) is an inaccurate value < X, and it is called (and here comes a novel concept) a fog.

Fogs are only approach to a given sum (what is called by you a limit).

For example: pi is a sum, and it is used by Standard Math as the limit of fog 3.14...[base 10], where fog 3.14...[base 10] < pi (fog 3.14...[base 10] only approaches sum pi).

In order to reach pi, one simply "jumps" form any arbitrary chosen scale level straight to sum pi, but then fog 3.14...[base 10] < pi is not found anymore, and we get a sum, which is based on finitely many segments AND points that have sum pi.

This novel reasoning about infinite convergent series is clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104.

In other words, sums are local numbers, and fogs are non-local numbers.

By OM the place value method is a fog if infinitely many scale levels are involved.

By Standard Math the place value method is a representation of a sum (fogs are not found under the Standard framework).

Since Standard Math paradigm does not deal with fogs, then X can't be but a sum.

By using the limited reasoning, one simply can't get X as a fog (called also a non-local number, under OM).
 
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jsfisher said:
Like it or not, nothing with limits in mathematics gets to the conclusion X both is > 0 and = 0. In your construction, X is always > 0, even in the limit.
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There is no "even in the limit" since the infinitely many scale levels of my construction are found exactly because the infinitely many added values (2a+2b+2c+2d+…) only approach X value, or in other words:

(2a+2b+2c+2d+…) < X, where < is an invariant fact.

On the contrary by Standard Math (2a+2b+2c+2d+…) = X, and since by my construction (2a+2b+2c+2d+…) is found as long as X is found, then if
X-(2a+2b+2c+2d+…)=0 (according to Standard Math) then X must be > 0 AND = 0 if (2a+2b+2c+2d+…) (which is found as long as X > 0) actually reaches X (and then X must be also 0 if (2a+2b+2c+2d+…) is still found also if it reaches X).

It is about the time for you to understand the difference between a sum and a fog (http://www.internationalskeptics.com/forums/showpost.php?p=5734631&postcount=9165).
 
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doronshadmi said:
...<snipped confused tangent>...

On the contrary by Standard Math (2a+2b+2c+2c+…) = X
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At the limit, yes.

...and since by my construction (2a+2b+2c+2c+…) is found as long as X is found
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"Is found"? It wasn't lost. It wasn't missing. The infinite sum simply is.

...then if X-(2a+2b+2c+2c+…)=0 (according to Standard Math) then X must be > 0 AND = 0
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Why? You've somehow jumped from an incorrect understanding of limits to a completely disconnected conclusion. X is a constant > 0 throughout. What nonsense are you claiming leads you to conclude that X must also be 0?

...if (2a+2b+2c+2c+…) (which is found as long as X > 0) actually reaches X (and then X must be also 0 if (2a+2b+2c+2c+…) is still found also if it reaches X).
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Would this be that nonsense? You have already admitted "by standard math" that (2a+2b+2c+2c+…) = X. Your disagreement with standard math doesn't change that that is the "by standard math" conclusion. So, clearly if (2a+2b+2c+2c+…) = X "by standard math", then of necessity X - (2a+2b+2c+2c+…) must = 0 "by standard math".

Nothing in those statements gets you to the conclusion X must be > 0 and = 0 "by standard math", though. Everything remains consistent with just X>0. Nothing implies X=0 also.

Again, doron, you only succeeded at another of your proof by misconception.
 
jsfisher said:
At the limit, yes.



"Is found"? It wasn't lost. It wasn't missing. The infinite sum simply is.



Why? You've somehow jumped from an incorrect understanding of limits to a completely disconnected conclusion. X is a constant > 0 throughout. What nonsense are you claiming leads you to conclude that X must also be 0?



Would this be that nonsense? You have already admitted "by standard math" that (2a+2b+2c+2c+…) = X. Your disagreement with standard math doesn't change that that is the "by standard math" conclusion. So, clearly if (2a+2b+2c+2c+…) = X "by standard math", then of necessity X - (2a+2b+2c+2c+…) must = 0 "by standard math".

Nothing in those statements gets you to the conclusion X must be > 0 and = 0 "by standard math", though. Everything remains consistent with just X>0. Nothing implies X=0 also.

Again, doron, you only succeeded at another of your proof by misconception.
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Since the infinite convergent series is found (2a+2b+2c+2c+…) upon infinitely many scale levels, as long as constant X>0 is found upon infinitely many scale levels, then (2a+2b+2c+2c+…) is considered as an infinite convergent series as long as it does not reach the value of constant X>0.

This is an irresistible logical fact about the infinite convergent series (2a+2b+2c+2c+…).

Since Standard Math insists that (2a+2b+2c+2c+…) is both infinite convergent series AND also has the exact value of X>0, then X must be also 0 in order to let the infinite convergent series (2a+2b+2c+2c+…) to reach the value of constant X>0.

Standard Math simply does not realize that claim that ((2a+2b+2c+2c+…) is an infinite convergent series) AND ( (2a+2b+2c+2c+…)=X ) is equivalent to the claim that X > AND = 0.

The reason to this false is based exactly on the indistinguishability between local and accurate values (that are reached by finitely many steps) and non-local an inaccurate values (that only approach by infinitely many steps).


The proof without words supports OM on this fine subject, and does not support Standard Math on this fine subject:

4430320710_daf5b36c0f_o.jpg


You ignored http://www.internationalskeptics.com/forums/showpost.php?p=5734631&postcount=9165.

Why is that?

jsfisher said:
"Is found"? It wasn't lost. It wasn't missing. The infinite sum simply is.
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Infinite AND sum is a logical contradiction.
 
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Here is a part of a paper that is based on the Standard notion of infinitely many elements (http://www.ucl.ac.uk/philosophy/academic-research/watling/papers/TheSumOfAnInfiniteSeries.pdf John Watling, The sum of an infinite series, Analysis 13 (1952 - 53), 39 – 46.) (another address:http://www.pdfqueen.com/html/aHR0cD...GVycy9UaGVTdW1PZkFuSW5maW5pdGVTZXJpZXMucGRm):

The mistake that the completion of an infinite sequence of acts is logically impossible might
also be explained in this way.

The requirement that however many acts have been done, more must remain, is thought to entail that more acts must always remain.

But when the requirement is put explicitly as “whatever finite number has been done, more must remain”, it is clear that it does not entail that after an infinite number have been done more must remain.
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By this part we can clearly see that Standard Math forces the notion of an accurate value (that is found by each finite step of infinitely many steps) on a value that is the result of infinitely many steps, by using the wrong notion "after" (or "all") in order to support the wrong notion that an infinite series has an accurate value exactly as a finite series of accurete values has an accurate value.

This logical failure is a direct result of Standard Math, which is tuned to deal only with accurate values, no matter what illogical payment is done, in order to achieve this goal.

Here is another part from this article:
It is important to distinguish this argument from another that is similar to it: Each of the additions that form the sum of 1 + ½ + ¼ + . . . gives a sum of a finite number of terms, e.g. ¼ to 1 + ½ gives a sum of three terms; since nothing else is required to form the sum of the series than making all these additions, the sum of the series must be a sum of a finite number of terms.

If this argument were valid we should have proved that the infinite series did not possess one of its defining properties, a contradiction from which it would follow that the sum did not exist.

But the argument is fallacious; it does not follow from the fact that each addition produces a certain result that all the additions together produce that result.

Because each of the additions yields a sum of a finite number of terms it does not follow that when all the additions are made they give a sum of a finite number of terms.

This is like arguing that the sum of an infinite number of the terms of a series must be equal to one of the terms of the sequence of sums of finite numbers of terms.
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Well, this is the whole point, an infinite number of the terms of a series do not have an accurate value (which is a property that only a finite number of the terms of a series has).

Again Standard Math forces accuracy on an infinite collection, no matter what illogical payment is done, in order to achieve this goal.

And another part of this article:
Now from the definition of a limit we proved that each addition of a term of a series of positive
terms brought the sum of the terms nearer to the limit. The addition of each term brings the sum nearer to the limit than the sum of the finite number of terms preceding that term.

Therefore the addition of all the terms, forming the sum of the series, gives a sum nearer to the limit than the sum of any finite number of terms.

Of course no single addition brings the sum nearer than every sum of a finite number of terms.

Now from the definition of a limit, given any positive number a sum of a finite number of terms may be found such that the absolute value of the difference between it and the limit is less than that positive number.

Therefore the absolute value of the difference between the sum and the limit is less than any positive number.

But if the difference between two fixed quantities is less than any positive number, then they are equal.

Therefore the sum of an infinite series, whose terms all have the same sign, is equal to the limit of the sequence of sums of its terms.
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Look what Standard Math does (the bolded part is mark by me):

It claims that there is a complete collection of positive numbers > 0, by examine each positive number and show that its value > 0.

By doing this Standard Math forces the accuracy that is found by each finite value, on a collection of infinitely many accurate values.

But it does not mean that if each member of some collection has an accurate value, then the value of infinitely many accurate values must be itself an accurate (or fixed) value.

So the whole notion of the Limit concept is based on a wrong notion.
 
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doronshadmi said:
No The Man.

X is an accurate value, called a sum.

(2a+2b+2c+2d+...) is an inaccurate value < X, and it is called (and here comes a novel concept) a fog.
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Once again Doron deliberately being inaccurate and inconsistent, as you are, is in no way a “novel concept”.

Are you now claiming that your ‘bended’ segments always add up to “X is an accurate value, called a sum” even when there are an infinite number of your ‘bended’ segments?

doronshadmi said:
Fogs are only approach to a given sum (what is called by you a limit).

For example: pi is a sum, and it is used by Standard Math as the limit of fog 3.14...[base 10], where fog 3.14...[base 10] < pi (fog 3.14...[base 10] only approaches sum pi).

In order to reach pi, one simply "jumps" form any arbitrary chosen scale level straight to sum pi, but then fog 3.14...[base 10] < pi is not found anymore, and we get a sum, which is based on finitely many segments AND points that have sum pi.

This novel reasoning about infinite convergent series is clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104.

In other words, sums are local numbers, and fogs are non-local numbers.

By OM the place value method is a fog if infinitely many scale levels are involved.

By Standard Math the place value method is a representation of a sum (fogs are not found under the Standard framework).

Since Standard Math paradigm does not deal with fogs, then X can't be but a sum.

By using the limited reasoning, one simply can't get X as a fog (called also a non-local number, under OM).
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Again what you call “Standard Math” deals quite well and with inaccurate values like estimates, rounded values and even ranges of values including their sums. A fact you would be well aware of if you had ever actually used what you call “Standard Math”. The only “fog” continues to be the one you deliberately restrict yourself to when it comes to what you call “Standard Math”.
 
doronshadmi said:
Since the infinite convergent series is found (2a+2b+2c+2c+…) upon infinitely many scale levels, as long as constant X>0 is found upon infinitely many scale levels, then (2a+2b+2c+2c+…) is considered as an infinite convergent series as long as it does not reach the value of constant X>0.
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"Is found"? You continue with the verbal nonsense. What do you mean by "is found"? Also, (2a+2b+2c+...) isn't "found" on infinitely many scale levels, either. It is an infinite series that has a single, precise value of X.

Be that as it may, X is a constant throughout your construction. The limit of X as the generation number approaches infinity is whatever constant value X started with at Generation 0. It does not change.

If Kn is the n-th generation Koch curve, and L(Kn) is the length of that curve, and W(Kn) is its width, then the limit as n approaches infinity of L(Kn) is X and of W(Kn) is 0.

Are you disputing these specific claims?

This is an irresistible logical fact about the infinite convergent series (2a+2b+2c+2c+…).
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In the confused and contradictory world of doronetics, perhaps. In real Mathematics, no.

Since Standard Math insists that (2a+2b+2c+2c+…) is both infinite convergent series AND also has the exact value of X>0, then X must be also 0 in order to let the infinite convergent series (2a+2b+2c+2c+…) to reach the value of constant X>0.
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By what miracle of logic do you get to that "then X must be also 0" conclusion? X is greater than 0. (2a+2b+2c+...) = X. That's all real Mathematics has to say about it. The rest you just made up.

[quoted]Standard Math simply does not realize that claim that ((2a+2b+2c+2c+…) is an infinite convergent series) AND ( (2a+2b+2c+2c+…)=X ) is equivalent to the claim that X > AND = 0.[/quote]

And yet you cannot explain why that is the case.
 
The Man said:
Are you now claiming that your ‘bended’ segments always add up to “X is an accurate value, called a sum” even when there are an infinite number of your ‘bended’ segments?
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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.


The Man said:
Again what you call “Standard Math” deals quite well and with inaccurate values like estimates, rounded values and even ranges of values including their sums.
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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.
 
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jsfisher said:
If Kn is the n-th generation Koch curve, and L(Kn) is the length of that curve, and W(Kn) is its width, then the limit as n approaches infinity of L(Kn) is X and of W(Kn) is 0.

Are you disputing these specific claims?
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L(Kn) 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.

“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.

jsfisher said:
By what miracle of logic do you get to that "then X must be also 0" conclusion? X is greater than 0. (2a+2b+2c+...) = X. That's all real Mathematics has to say about it. The rest you just made up.
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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.
 
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ddt said:
I thought you didn't do infinite sets.
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An infinite set does not have an accurate size, very simple.

Please be aware of the fact that I did not say "the set of all natural numbers".
 
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doronshadmi said:
An infinite set does not have an accurate size, very simple.

Please be aware of the fact that I did not say "the set of all natural numbers".
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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"?
 
doronshadmi said:
Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...)...
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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.
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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.
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Exactly right, nor is an irrelevant analogy relevant.
 
doronshadmi said:
L(Kn) 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.
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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.
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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.
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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.
 
sympathic said:
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"?
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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.
 
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jsfisher said:
Stop right there. There are no "each values". A convergent infinite series (with the adjectives properly ordered) has one and only one value.
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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.

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

jsfisher said:
Exactly right, nor is an irrelevant analogy relevant.
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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).
 
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jsfisher said:
Then why did you make the idiotic claim that X must be simultaneously greater than 0 and equal to 0?
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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.

jsfisher said:
So, why didn't you just say you don't like limits,
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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.

jsfisher said:
Mind you, though, real Mathematics has no such trouble,
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Because what you call real Mathematics deals only with accurate (fixed) values.

jsfisher said:
Time to move on to the next topic you don't understand.
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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.
 
doronshadmi said:
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.
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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?
 
doronshadmi said:
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.
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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.
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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).
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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.
 
sympathic said:
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?
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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.
 
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jsfisher said:
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.
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doronshadmi said:
jsfisher said:
doronshadmi said:
Again, it does not mean that if each value of the infinite convergent series (2a+2b+2c+2d+...)...
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Stop right there. There are no "each values". A convergent infinite series (with the adjectives properly ordered) has one and only one value.
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Exactly jsfisher, the convergent infinite series has an inaccurate value, which is a property that is different than any given part of that series.
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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:
doronshadmi said:
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.
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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.

jsfisher said:
You are on a roll here for your own personal failures.
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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.
 
doronshadmi said:
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.
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Strange, I thought you did not believe in limits.
 
doronshadmi said:
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
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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 said:
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.
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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).
 
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sympathic said:
Strange, I thought you did not believe in limits.
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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.
 
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jsfisher said:
doronshadmi said:
Because by your idiotic reasoning the bended constant X > 0 must be also = 0 in order enable (2a+2b+2c+2d+...) to be X.
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You repeat this idiotic claim, yet you cannot demonstrate it. Why is that?
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Let us carefully research who's claim is right, on this case.

Here is the considered diagram:

4464201033_30e7dbd8d4_o.jpg


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).
 
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doronshadmi said:
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.
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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?



doronshadmi said:
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.
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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.
 
The Man said:
So now your “X” is not “an accurate value
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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).




The Man said:
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.
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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.
 
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doronshadmi said:
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).
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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.
 
The Man said:
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.
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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.
 
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