Deeper than primes

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jsfisher said:
How about we just set aside your gibberish and assume you meant for Steps 2 and 3 that we applied Koch's procedure and then shrunk it by 3/4 to hold the overall length of the result constant.
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You're right jsfisher, ¾ would be the correct scale factor, I should have double checked. I apologize to everyone for my previous error.
 
The Man said:
You're right jsfisher, ¾ would be the correct scale factor, I should have double checked. I apologize to everyone for my previous error.
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It does not change these facts:

X = the constant length > 0

4430320710_daf5b36c0f_o.jpg


1) By Standard Math X – (2a+2b+2c+2d+…) = 0

2) (1) is false because (2a+2b+2c+2d+…) can be found as long as X is found.

3) Since X is found upon infinitely many scale levels then (2a+2b+2c+2d+…) must be < X , and as a result X - (2a+2b+2c+2d+…) > 0.

4) Conclusion: (2a+2b+2c+2d+…) does not have sum X.
 
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doronshadmi said:
As I said, you simply can't get that X-(2a+2b+2c+2d+...) > 0 as proved in http://www.internationalskeptics.com/forums/showpost.php?p=5715516&postcount=9032 by using a proof without words (http://en.wikipedia.org/wiki/Proof_without_words).

Your rambling will not help you here, jsfisher.
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You simply can't get that you have again failed, as proven in http://www.internationalskeptics.com/forums/showpost.php?p=5715127&postcount=9025.

You gibberish and tangents cannot save you, doronshadmi.
 
doronshadmi said:
How sad that you can't get http://www.internationalskeptics.com/forums/showpost.php?p=5715516&postcount=9032 or http://www.internationalskeptics.com/forums/showpost.php?p=5715530&postcount=9033.
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Not nearly as sad as those posts.



doronshadmi said:
So what?

Also a non-accurate value has self similarity.
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Well that’s one aspect of the proof you are not disputing, care to try the other two?




doronshadmi said:
You still do not get it do you?

So let us improve the proof without words, by using Koch's fractal.

1) Take a straight 1-dim with length X.

2) Bend it and get 4 equal sides along it.

3) Since the length between the opposite edges is changed to the sum of only 3 sides, and since the number of the sides after the first bending is 4 sides, we have to multiply the bended 1-dim element by 1/(the number of the bended sides), in order to get back length X.

As a result the bended 1-dim element has length X, but the length between its opposite edges becomes smaller (it converges).

In general, this convergent series of 1/(the number of the bended sides) is resulted by 1/1+1/4+1/16+1/64+1/256+... , where X is subtracted by (2a+2b+2c+2d+…)

Here is the result:

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]


4) By Standard Math X – (2a+2b+2c+2d+…) = 0


5) (4) is false because (2a+2b+2c+2d+…) can be found as long as X is found.

6) Since X is found upon infinitely many scale levels then (2a+2b+2c+2d+…) must be < X , and as a result X - (2a+2b+2c+2d+…) > 0.

7) Conclusion: (2a+2b+2c+2d+…) does not have sum X.
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Well other then your usual sloppiness as already noted by jsfhisher I’ll just add what again you're lacking the sums “By Standard Math”.

Your first series “1/1+1/4+1/16+1/64+1/256+...” has a common ratio of ¼ and starts with the value 1/1 making the difference between the 4 times series and the original just 4. Thus the sum of the original series (s) is 4s-s = 4 or s(4-1) = 4 or s = 4/3.

Your second series lacks quite a bit of information (perhaps deliberately) as “(2a+2b+2c+2d+…)” from the diagram is it apparent that you intended the elements of the series to represent the differences in the separation of your end points from the previous iteration to the next. Unfortunately your description of your construction is also seriously lacking in information. However you do specifically refer to “Koch's fractal” so again using the appropriate construction for the Koch curve and scaling down by ¾ to maintain your “X” value we can develop the series relations. Since the scale factor is ¾ your first value of this series would be the difference (your “2a”) of that scaled down figure from your initial figure (X). So the first term in this series is X-3X/4 or just X/3. Your second term (your “2b”) repeats the same procedure with the previous values and results in 3X/4-9X/16 or 12X/16-9X/16 or just 3X/16. The fourth term (your “2c”) repeats the same procedure with the previous values and results in 9X/16-27X/64 or 36X/64-27X/64 or just 9X/64. Giving a common ratio for the series of 9/16, so the difference between the 16/9 series and the original would be 16X/27. Making the sum (s) as 16s/9-s= 16X/27 or s(16/9-9/9) = 16X/27 or s = (16X/27) / (7/9) or 144X/189 or just 16X/21. Masking X – 16X/21 = 5X/21. Of course I could have made a mistake in the calculations somewhere, but I’ll leave that to you to figure out.
 
doronshadmi said:
It does not change these facts:

X = the constant length > 0

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

1) By Standard Math X – (2a+2b+2c+2d+…) = 0

2) (1) is false because (2a+2b+2c+2d+…) can be found as long as X is found.

3) Since X is found upon infinitely many scale levels then (2a+2b+2c+2d+…) must be < X , and as a result X - (2a+2b+2c+2d+…) > 0.

4) Conclusion: (2a+2b+2c+2d+…) does not have sum X.
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Your speculations still do not constitute facts.
 
doronshadmi said:
It does not change these facts:

X = the constant length > 0

1) By Standard Math X – (2a+2b+2c+2d+…) = 0
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What are you on about? It sure looks like you want to say the "width" of your little drawing is 0 in the limit. Why don't you just say that rather than all this nonsense, misdirection, and confusion on your part?

2) (1) is false because (2a+2b+2c+2d+…) can be found as long as X is found.
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Neither were ever missing, so what are you going on about now? Nothing you are saying, here, invalidates (1). Nor are you in any way expressing any understanding of limits.

3) Since X is found upon infinitely many scale levels then (2a+2b+2c+2d+…) must be < X , and as a result X - (2a+2b+2c+2d+…) > 0.
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No, this is completely wrong. The limit of the "width" of the generations is zero. If you insist on making this as contorted as possible, then yes, too the limit of the sum of all the little pieces cut off with each new generation (that would be your 2a+2b+2c+... series) is X.

4) Conclusion: (2a+2b+2c+2d+…) does not have sum X.
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Nope. Another big failure on your part. The infinite series does in fact have X for its value. You have done nothing to show otherwise. You have only assumed it isn't then insisted it can't be.

Too bad for you it doesn't listen.
 
The Man said:
You're right jsfisher, ¾ would be the correct scale factor, I should have double checked. I apologize to everyone for my previous error.
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The misstated scale factor isn't all that important. Doron's acceptance of the wrong value was amusing, but of no real consequence.

I had thought doron was trying to explore--as clumsily as ever--an apparent paradox. In his original construction (of snowflake inscribed in a circle), the area bounded by the snowflake vanishes to 0 in the limit while the perimeter remains constant. (Or, equivalently, the width of his curve becomes 0 while the length remains constant).

But no, he didn't do that. Instead, he used Koch as just another convoluted way to say he believes infinite series never really reach their limit.
 
jsfisher said:
The misstated scale factor isn't all that important. Doron's acceptance of the wrong value was amusing, but of no real consequence.
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No not all that important to the general discussion, but I do like to keep my values and calculations accurate.


jsfisher said:
I had thought doron was trying to explore--as clumsily as ever--an apparent paradox. In his original construction (of snowflake inscribed in a circle), the area bounded by the snowflake vanishes to 0 in the limit while the perimeter remains constant. (Or, equivalently, the width of his curve becomes 0 while the length remains constant).
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As I indicated before that might be an interesting problem and discussion, but unfortunately the specificity and rigor needed to explore it is simply beyond anything he is apparently capable of adhering to.

jsfisher said:
But no, he didn't do that. Instead, he used Koch as just another convoluted way to say he believes infinite series never really reach their limit.
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Not to mention how he keeps vacillating (for a convergent series) between it has no sum, it has no limit, the sum is less than the limit and now the new, improved and equally ineffective dodge that some rounded off representation of that sum “is not an accurate value”.
 
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jsfisher said:
Nope. Another big failure on your part. The infinite series does in fact have X for its value. You have done nothing to show otherwise.
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No, X > (2a+2b+2c+2d+...) exactly because (2a+2b+2c+2d+...) is found only if X is found.

X > 0 and by your Limit-oriented reasoning X > AND = 0 , which is a contradiction.

Jsfisher, you simply do not get the rigours proof without words (http://en.wikipedia.org/wiki/Proof_without_words) in http://www.internationalskeptics.com/forums/showpost.php?p=5717208&postcount=9043 exactly because it is beyond your formal training.

The following fact is beyond your obsolete Limit-oriented reasoning:

4430320710_daf5b36c0f_o.jpg
 
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The Man said:
Not to mention how he keeps vacillating (for a convergent series) between it has no sum, it has no limit,
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Speak for yourself The Man.

The converges series (2a+2b+2c+2d+...) only approaches X and therefore can’t reach (can’t have) its value (and therefore does not have an accurate sum, which is a notion that you clearly can't comprehend all along this thread).

Since (2a+2b+2c+2d+...) only approaches X it does not have sum=X, exactly because that is only approaches, has no limit.
 
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jsfisher said:
No, this is completely wrong. The limit of the "width" of the generations is zero.
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“width” zero is a value that can’t be reached as long as X > 0 is a constant value upon infinitely many scale levels, and this is exactly the fact about constant X > 0.

jsfisher said:
If you insist on making this as contorted as possible, then yes, too the limit of the sum of all the little pieces cut off with each new generation (that would be your 2a+2b+2c+... series) is X.
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The sum of all pieces cut off with each new generation does not exist.

It is incomplete (it is not an accurate value) exactly because X > 0 is a constant upon infinitely many scale levels.

Your “sum of all the little pieces cut off with each new generation” is false exactly as X > AND = 0 is false, and you, jsfisher, you are the on who insists that X > AND = 0 is true, in order to fit the results to your obsolete Limit-oriented notion.
 
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doronshadmi said:
Jsfisher, you simply do not get the rigours proof without words (http://en.wikipedia.org/wiki/Proof_without_words) in http://www.internationalskeptics.com/forums/showpost.php?p=5717208&postcount=9043 exactly because it is beyond your formal training.

The following fact is beyond your obsolete Limit-oriented reasoning:
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Inferiority issues again Doron? Do you think that mathematicians are production workers at a manufacturing factory that are only proficient in procedures they received training on? give the posters in this thread a bit more credit, you do not get a math degree at the supermarket.
 
doronshadmi said:
Speak for yourself The Man.

The converges series (2a+2b+2c+2d+...) only approaches X and therefore can’t reach (can’t have) its value (and therefore does not have an accurate sum, which is a notion that you clearly can't comprehend all along this thread).

Since (2a+2b+2c+2d+...) only approaches X it does not have sum=X, exactly because that is only approaches, has no limit.
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You clearly do not understand what a limit is. You are talking to yourself. You don't get to define what a limit is.
 
sympathic said:
Inferiority issues again Doron? Do you think that mathematicians are production workers at a manufacturing factory that are only proficient in procedures they received training on? give the posters in this thread a bit more credit, you do not get a math degree at the supermarket.
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Training (in any subject) is a lifetime story, sympathic.

In your case sympathic, jsfisher and The Man, your training is based on a fundamental failure, which its rooted are found 2,300 years ago, and OM corrects it.
 
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sympathic said:
You clearly do not understand what a limit is. You are talking to yourself. You don't get to define what a limit is.
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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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doronshadmi said:
Training (in any subject) is a lifetime story, sympathic.

In your case sympathic, jsfisher and The Man, your training is based on a fundamental failure, which its rooted are found 2,300 years ago, and OM corrects it.
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This fundamental failure is what made everything you see around you possible. What have you been able to achieve using your OM? and spare us the ethics/voodoo ramblings. Your counter-productive and fixated (sometimes even destructive) approach as it comes across in your posts shows that either OM is not what you think it is, or that even you do not get it.
 
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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I'm not forcing anything, just using universal definitions and concepts. Your childish interpretation of this concept makes the limit concept as you understand it redundant. Too bad you do not listen to anyone but your imagination. Try it sometimes, you may actually learn something that can be of use.
 
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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Stop flattering yourself. You have achieved nothing, you have taught us nothing, your OM is useless, it is not even a consistent set of ideas. It is just gibberish and pretty drawings. Stop bothering others with your nonsense if you do not wish to learn. Stop using others to further convolute your twisted understanding of universal mathematical concepts. You are not a genius, at least when it comes to math, you are not the messiah of math.
 
doronshadmi said:
“width” zero is a value that can’t be reached as long as X > 0 is a constant value upon infinitely many scale levels, and this is exactly the fact about constant X > 0.
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Nope, not a fact. Just another doron baseless assumption. The limit of the width is 0, and the limit of the length is X.

If you can prove otherwise (that's prove, not just assert and assume), please do so, but you will fail in the attempt.

Just out of interest, doron, do you have any idea what are the following limits?

Let F(x) = x/x. What is the limit of F(w) as w approaches 0?

Let F(x) = 1 when x=0 and F(x) = 0 everywhere else. (So, F is a "spike" function.) What is the limit of F(w) as w approaches 0?

Let F(x) = 1 when x>0, F(x) = 0 when x<0, and undefined when x=0. (F is a step function.) What is the limit of F(w) as w approaches 0? What is the limit of F(w) as w approaches 0 from the right (i.e. w>0)? What is the limit of F(w) as w approaches 0 from the left?

Consider the surface of revolution generated by y=1/x revolved about the X-axis. What is the surface area of the surface from x=1 to infinity? What is its volume?
 
sympathic said:
This fundamental failure is what made everything you see around you possible. What have you been able to achieve using your OM? and spare us the ethics/voodoo ramblings. Your counter-productive and fixated (sometimes even destructive) approach as it comes across in your posts shows that either OM is not what you think it is, or that even you do not get it.
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1) The "ethics/voodoo ramblings" is a direct result of your limited formal training of this subject.

2) I do not need more than OM's proof without words in order to show how your "reasoning" is based on X > and = 0.
 
doronshadmi said:
1) The "ethics/voodoo ramblings" is a direct result of your limited formal training of this subject.

2) I do not need more than OM's proof without words in order to show how your "reasoning" is based on X > and = 0.
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As always, you did not address the core of my post, but rather hijacked it to further discuss your convoluted ideas. Is this your idea of a conversation?
 
jsfisher said:
Why do you assume that? It isn't at all true, so why did you make it up?
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Because it is true.

You simply do not have any understanding of the real nature of infinitely many added and convergent values, exactly as shown in the case of (2a+2b+2c+2d+...), whish only approach and can’t reach the value of the limit.
 
jsfisher said:
Nope, not a fact. Just another doron baseless assumption. The limit of the width is 0, and the limit of the length is X.

If you can prove otherwise (that's prove, not just assert and assume), please do so, but you will fail in the attempt.
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The proof without words:

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

The days of your X > AND = 0 reasoning are over, and you can’t do anything about this fact.
 
sympathic said:
No it is not. If at all the proper way to write what you meant is "X>0 AND X=0" but you don't even understand that.
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You did not change the simple fact that X is based on a wrong reasoning, if your Limit-oriented reasoning is used.
 
doronshadmi said:
You did not change the simple fact that X is based on a wrong reasoning, if your Limit-oriented reasoning is used.
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Nor did I attempt to. I just claimed that writing coherent and consistent statements is imperative in Math. But you don't do math - you do drawings.
 
doronshadmi said:
The proof without words:

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

The days of your X > AND = 0 reasoning are over, and you can’t do anything about this fact.
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More accurately it is a proof without proof. But why all of a sudden the need to prove? what happened to "direct perception". Doron Shadmi: "I have a feeling it is true, therefore it is true".
 
sympathic said:
Nor did I attempt to. I just claimed that writing coherent and consistent statements is imperative in Math. But you don't do math - you do drawings.
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This is simply wrong since "X > AND = 0" has exactly the same meaning as "X > 0 AND X=0".

You are invited to prove that this is not the case.
 
sympathic said:
More accurately it is a proof without proof. But why all of a sudden the need to prove? what happened to "direct perception". Doron Shadmi: "I have a feeling it is true, therefore it is true".
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Dirrect perception is the common source of both feeling and logical reasoning.

You have asked for a proof in your terms, I provided one by using a proof without words.

Your Limit-oriented obsolete reasoning can't comprehend it.

Very simple, you can’t grasp the fact that it has been proven that (2a+2b+2c+2d+...) < X.
 
doronshadmi said:
Dirrect perception is the common source of both feeling and logical reasoning.

You have asked for a proof in your terms, I provided one by using a proof without words.

Your Limit-oriented obsolete reasoning can't comprehend it.

Very simple, you can’t grasp the fact that it has been proven that (2a+2b+2c+2d+...) < X.
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The only thing I have ever asked is for you to learn maths properly, and leave us all alone until you do.
 
sympathic said:
The only thing I have ever asked is for you to learn maths properly, and leave us all alone until you do.
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Do you mean your Limit-oriented obsolete reasoning?

Let us leave it to the historians, it is not relevant anymore.
 
sympathic said:
Nor did I attempt to. I just claimed that writing coherent and consistent statements is imperative in Math. But you don't do math - you do drawings.
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Writing is nothing but some particular way to express a notion, exactly as a diagram is another particular way to express a notion.

In both cases the notion is the important thing, and not any particular expression of it.

Your reply is another example of the destructive influence of your formal training on your abstraction abilities.

Your teachers washed your brain with the slogan that “writing ... is imperative in Math” until you are not able the get coherency and consistency if it is expressed by a diagram.
 
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