Deeper than primes

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doronshadmi said:
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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Mathematics is not about expressing notions. Art is. You are an artist not a mathematician. Why do you even want to be one? is it because you are trying to prove something to yourself? if so it can not be accomplished by drawing. not in math anyway. Tough luck.
 
sympathic said:
I can comprehend that YOUR proof without words does not constitute a proof. I am not really sure you know what a proof is.
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clearly you can't.

Your Limit-orineted reasoning is based on X > AND = 0 , and from this false point of view you can't get anything.
 
doronshadmi said:
clearly you can't.

Your Limit-orineted reasoning is based on X > AND = 0 , and from this false point of view you can't get anything.
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Ok, you win. Our reasoning is limited and obsolete. Math as we know it is dead and useless. Long live OM. Happy?
 
doronshadmi said:
Speak for yourself The Man.
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Have you finally made up your mind what you want to claim then?


doronshadmi said:
The converges series (2a+2b+2c+2d+...) only approaches X and therefore can’t reach (can’t have) its value
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So the sum is always less than the limit.

doronshadmi said:
(and therefore does not have an accurate sum, which is a notion that you clearly can't comprehend all along this thread).
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Or the sum is just not “accurate”.

doronshadmi said:
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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Or it “does not have sum” and “has no limit”.

Well Doron when you finial figure out how to speak for yourself, please let us know.
 
zooterkin said:
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.
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Congratulations, you now have a square.
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doronshadmi said:
EDIT:

Where is the square in _/\_ ?
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How do steps 1 and 2 give you _/\_ ?

You give no definition of the angles of your bends, and you refer to the resultant figure having 4 sides which normally indicates a closed figure. A closed figure with four equal sides is a square.
 
The Man said:
Have you finally made up your mind what you want to claim then?




So the sum is always less than the limit.



Or the sum is just not “accurate”.



Or it “does not have sum” and “has no limit”.

Well Doron when you finial figure out how to speak for yourself, please let us know.
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Sum = accurate value

Inaccurate value ≠ Sum

Simple, isn't it?
 
sympathic said:
Ok, you win. Our reasoning is limited and obsolete. Math as we know it is dead and useless. Long live OM. Happy?
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Math as you know it works very good as a finite system, which has beautiful finite results.

If you wish to deal with the real complexity of the infinite, you first have to understand its qualitative atomic aspects which enables it, such that any infinite result of these aspects can't reach the completeness of the atomic quality.

In other words, approaches is an invariant property of any infinite complexity, such that w ≠ 0 and F(w) has no limit.

Infinite interpolation\extrapolation are valid concepts of the mathematical science, and they do not hide any behind the Limit-oriented curtain.
 
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doronshadmi said:
The proof without words proof:

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

The days of your X > AND = 0 reasoning are over, and you can’t do anything about this fact.
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Oh, dear! Who ever alleged that X = 0, in the limit or otherwise? X is now and has always been the length of each of your generations. It's a constant and greater than 0.

Why do you say so many wrong things?
 
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doronshadmi said:
jsfisher said:
What is the limit of F(w) as w approaches 0?
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If approaches is a constant property, then w > 0 and F(w) has no limit.
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"If approaches is a constant property"? Did you mean that in any way that should make sense, or did you include it to emphasize your total misunderstanding of limits in Mathematics.

(We can all assume doronetics has an entirely novel and inconsistent treatment of limits, but the context here is within real Mathematics.)

And why do you assume w must be greater than 0? Are you so limited in your thinking that all the negative numbers must be ignored?
 
jsfisher said:
And why do you assume w must be greater than 0? Are you so limited in your thinking that all the negative numbers must be ignored?
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No problem.

If approaches is a constant property, then w ≠ 0 and F(w) has no limit.

By your "reasoning" X ≠ AND = 0.
 
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jsfisher said:
(We can all assume doronetics has an entirely novel and inconsistent treatment of limits, but the context here is within real Mathematics.)
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Wow.

Jsfisher is the voice of the choir in some Sophocles' tragedy.
 
doronshadmi said:
Again your step-by-step reasoning? (maybe a better name is stop-by-stop).
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The steps were provided by you, not me. The fact they didn't agree with your drawing is your problem, and yours alone. Don't blame any of us for your failures.
 
jsfisher said:
Prove my statement wrong. Do show us how limits work in doronetics.
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Here is the right way to get the value (and the concept) of Limit.

Two sizes of the same incompleteness have result 0 if they are subtracted from each other.

The real problem here is 1 – (1/2+1/4+1/8+…) and Archimedes did prove that it = 0.

The self similarity over scales clearly shown also by the following diagram, where the values 1,2,4,8,16,32,… etc. are not reached, ad infinituum:

4405947817_0146693fb4_o.jpg


In other words:

1 – (1/2+1/4+1/8+1/16+…) > 0

2 - (1/1+1/2+1/4+1/8+...) > 0

4 - (2/1+1/1+1/2+1/4+...) > 0

...

etc. ad infinituum.


If one reaches the value of the limit, then one does not use an infinite convergent series, because in order to reach the limit's value one uses for example:

1 – (1/2+1/4+1/8+2*(1/16)) = 0

2 - (1/1+1/2+1/4+2*(1/8+)) = 0

4 - (2/1+1/1+1/2+2*(1/4)) = 0

... etc. , where the multiplication by 2 can be done in any wished place, which breaks the convergent series, in order to reach the value of the limit.

In other words, an infinite convergent series is found as long as it does not reach the value of the limit.
 
doronshadmi said:
Here is the right way to get the value (and the concept) of Limit....
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No, stop. Quit telling us about how others got it wrong. Quit drawing stupid pictures. Quit going off on tangents.

Focus, doron. Focus.

The task at hand is to explain how limits are defined in doronetics.

I know quite well how they work in Mathematics, and how they can be used to produce consistent and useful results. Now, how do you define limits in your little private world of OM?

...or will this be yet another thing you can't define, explain, or express in any consistent way?
 
doronshadmi said:
Sum = accurate value

Inaccurate value ≠ Sum

Simple, isn't it?
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Simply not true, is all it is.

We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy, for a multitude of purposes. You have never actually used math for anything (other than your fantasies) have you?
 
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The Man said:
Simply not true, is all it is.

We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy, for a multitude of purposes. You have never actually used math for anything (other than your fantasies) have you?
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Let me help you.

There are at least two kinds of numbers under OM:

1) Local numbers that have accurate values.

2) Non-local numbers that do not have accurate values.

For example pi(= circumference/diameter) is a local number under OM.

3.14159265...[base 10] is a non-local number that does not have an accurate value.

jsfisher said:
No, stop. Quit telling us about how others got it wrong. Quit drawing stupid pictures. Quit going off on tangents.

Focus, doron. Focus.

The task at hand is to explain how limits are defined in doronetics.

I know quite well how they work in Mathematics, and how they can be used to produce consistent and useful results. Now, how do you define limits in your little private world of OM?

...or will this be yet another thing you can't define, explain, or express in any consistent way?
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You may say that the limit of the non-local number 3.14159265...[base 10], is the local number pi, such that 3.14159265...[base 10] < pi.

By using this non-trivial notion, you may say that 3.14159265...[base 10] is similar to a virtual particle w.r.t to a non-virtual particle.

In other words, any local number is surrounded by non-local numbers, exactly as a non-virtual particle is surrounded by virtual particles.
 
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The Man said:
We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy
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In that case you do not distinguish, for example, between the accurate results of values like 3.1, 3.14, 3.141, 3.1415, 3.14159, ... ([base 10]) and the inaccurate result 3.14159...[base 10].

Non of these values above (accurate or inaccurate) are the accurate value pi(= circumference/diameter).
 
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doronshadmi said:
Math as you know it works very good as a finite system, which has beautiful finite results.

If you wish to deal with the real complexity of the infinite, you first have to understand its qualitative atomic aspects which enables it, such that any infinite result of these aspects can't reach the completeness of the atomic quality.

In other words, approaches is an invariant property of any infinite complexity, such that w ≠ 0 and F(w) has no limit.

Infinite interpolation\extrapolation are valid concepts of the mathematical science, and they do not hide any behind the Limit-oriented curtain.
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Your arrogance and confidence you have in the gibberish you write is just overwhelming. You haven't got a clue. In "real" math (not in Doron's fantasy math) infinity is a relative concept. In Statistics for example relatively small numbers (500 or even 30 in some cases) can be considered as infinity. Statistical theory as other branches of Math relies on limits.

You never learn and never will. How sad for you.
 
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sympathic said:
In "real" math ... infinity is a relative concept.
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If you ask Cantor he will tell you that infinity is an actual concept, which is not potential and not relative, because aleph0 is accurate exactly as 1 is accurate.

Sympathic you simply using words without any notion behind them, because you do not understand the real difference between infinite complexity which is relative, potential and inaccurate w.r.t the non-local and local atomic aspects, where non-locality is the actual infinity (notated as ∞) and locality is the actually finite (notated as 0).

By understanding the complex result of the linkage between the qualities of actual infinity (which is not the Cantorean actual infinity, which is a complex) and the actually finite, both Transfinite system and Infinitesimal system are changed by a paradigm-shift.

You may choose to work only under the standard paradigm, but this is your limited choice, not mine.

sympathic said:
Your arrogance and confidence you have in the gibberish you write is just overwhelming.
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Your Limit-oriented reasoning is underwhelming.
 
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doronshadmi said:
If you ask Cantor he will tell you that infinity is an actual concept, which is not potential and not relative, because aleph0 is accurate exactly as 1 is accurate.

Sympathic you simply using words without any notion behind them, because you do not understand the real difference between infinite complexity which is relative, potential and inaccurate w.r.t the non-local and local atomic aspects, where non-locality is the actual infinity (notated as ∞) and locality is the actually finite (notated as 0).

By understanding the complex result of the linkage between the qualities of actual infinity (which is not the Cantorean actual infinity, which is a complex) and the actually finite, both Transfinite system and infinitesimal system are changed by a paradigm-shift.

You may choose to work only under the standard paradigm, but this is your limited choice, not mine.
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I can't ask Cantor. He has been dead for nearly 92 years. Maybe you can through one of the uses of your direct perception. Even if I could I am sure this is not the answer I would get. His greatest accomplishment is perfectly aligned with what I have written. You refuse to learn anything from anyone but yourself - not a very productive approach.
 
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sympathic said:
I can't ask Cantor. He has been dead for nearly 92 years.
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Really?? Thank you for this information (come on sympathic don't be lazy and look over the internet about Cantor and Actual infinity).

sympathic said:
His greatest accomplishment is perfectly aligned with what I have written. You refuse to learn anything from anyone but yourself - not a very productive approach.
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On the contrary, I distinguish between approach and reach. You can't, partially thanks to the Cantorean Transfinite system.
 
sympathic said:
How exactly is this related to what I wrote?
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This part:

doronshadmi said:
If one reaches the value of the limit, then one does not use an infinite convergent series, because in order to reach the limit's value one uses for example:

1 – (1/2+1/4+1/8+2*(1/16)) = 0

2 - (1/1+1/2+1/4+2*(1/8+)) = 0

4 - (2/1+1/1+1/2+2*(1/4)) = 0

... etc. , where the multiplication by 2 can be done in any wished place, which breaks the convergent series, in order to reach the value of the limit.

In other words, an infinite convergent series is found as long as it does not reach the value of the limit.
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In order to understand it please read all of http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104.
 
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doronshadmi said:
Really?? Thank you for this information (come on sympathic don't be lazy and look over the internet about Cantor and Actual infinity).


On the contrary, I distinguish between approach and reach. You can't, partially thanks to the Cantorean Transfinite system.
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You don't get to tell me what I can or can't do.
 
doronshadmi said:
You can't get OM.

You see? I can.
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I get what you do not. What you call OM is a mountain of gibberish spun out of a graphical representation of Integer partitions. Your futile attempts at driving more substance out of it are in vain.
 
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