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.
 
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