Deeper than primes

[The Man]

Standard math is what doron likes it to be. Exactly like everything else with him. What matters in the end is what he thinks. You can not change that. I doudbt this will ever be any different with him. Too bad for him things are different in the real world.

Unfortunately and that’s the sad part, these really aren’t very difficult concepts, but Doron simply seems to prefer his own fantasies.

 

[doronshadmi]

Once again Doron if 0 (or 2*0) is one of your “added accurate values” then the sum of your “series” must have already been “X” before you added zero to it. Once again Doron, in case you still do not understand, adding 0 does not change a value. So if it is equal to “X” after you add 0 then it must have been equal to “X” before you added 0.

The Man, you simply can't get the fact that if 2*0 is one of the added values, then (2a+2b+2c+2d+…) is a finite series, which its sum is indeed X.

This is not the case if (2a+2b+2c+2d+…) is an infinite series, and in that case 2*0 is not one of the added values and as a result (2a+2b+2c+2d+…) < X exactly because any value of (2a+2b+2c+2d+…) is derived from the invariant X>0 up infinitely many bended levels.

 

[jsfisher]

Ho yes they are ( http://en.wikipedia.org/wiki/Proof_without_words ).

Perhaps you should actually read the references you cite. From the second sentence: Such proofs can be considered more elegant than...mathematically rigourous proofs

I say you are wrong; wikipedia says you are wrong. "Proof without words" are not rigorous proofs.

ETA: ...and your attempt doesn't even qualify as a proof without words.

Converges to X yes, reaches X no.

Again you demonstrate your lack of understanding of mathematics and mathematical terminology. (Hint: There are limits involved here, and we already know you can't cope with such things.)

This is not a suggestion jsfisher, 2*0 is one of the added values if (2a+2b+2c+2d+…) = X

Oh, yeah? Which term is that? Are you going to run from this question, too? It is equivalent to the "when is Y = 0?" question that scares you so.

Will this one scare you off, too?

...but then (2a+2b+2c+2d+…) is a finite series that has a sum (= X).

Um, no. It is an infinite series, and its value is X.

 

[The Man]

The Man, you simply can't get the fact that if 2*0 is one of the added values, then (2a+2b+2c+2d+…) is a finite series, which its sum is indeed X.

This is not the case if (2a+2b+2c+2d+…) is an infinite series, and in that case 2*0 is not one of the added values and as a result (2a+2b+2c+2d+…) < X exactly because any value of (2a+2b+2c+2d+…) is derived from the invariant X>0 up infinitely many bended levels.

Doron you simply can’t get the fact that adding 0 does not change a sum, whether it is the sum of a finite series or an infinite series. So once again your erroneous assertions are simply based on your ignorance (deliberate or otherwise) of mathematics, in this case the fact that zero is the additive identity.

 

[doronshadmi]

Doron you simply can’t get the fact that adding 0 does not change a sum, whether it is the sum of a finite series or an infinite series. So once again your erroneous assertions are simply based on your ignorance (deliberate or otherwise) of mathematics, in this case the fact that zero is the additive identity.

Let us use the terminology of Standard Math (including the term "all" about a given class), in order to demonstrate the failure of Standard Math within its own context, about the argument that the infinite convergent series (2a+2b+2c+2d+…) = X, where X is a constant and accurate value > 0.

It is obvious that any accurate value of the infinite convergent series (2a+2b+2c+2d+…) is the result of the projection of the different ends of any given bended form of the class of all bended forms of constant X>0 accurate value, upon the non-bended form of constant X>0.

Since any bended form of X has two different ends, then 2*0 is not one of the projections of the class of all bended forms of constant X>0 upon the non-bended form of constant X>0.

As a result the two different ends are an essential property of both [the class of all bended forms of constant X>0 accurate value] AND [the infinite convergent series (2a+2b+2c+2d+…), which is the result of the projection of the different ends of any given bended form of the class of all bended forms of constant X>0 accurate value, upon the non-bended form of constant X>0].

Conclusion: the result of the added accurate values of all projections that are derived from the class of all bended forms of constant X>0 upon the non-bended form of constant X>0, can't be but < constant X>0.

This proof is rigorously seen by the following proof without words:

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

The Man, you simply can't get the fact that all added elements "before" 2*0 are > 0, and as a result there is an unclosed gap between the class of all bended forms of constant X>0 accurate value, and its projection ( which is exactly the infinite convergent series (2a+2b+2c+2d+…) ) upon the non-bended form of the constant and accurate value X>0.

We rigorously proved that we can't conclude that if all the added values of the infinite convergent series (2a+2b+2c+2d+…) are accurate, then the value of this added accurate values, is also accurate, even if all infinitely many added accurate values are included (no accurate value is missing).

The set of all oranges is not itself and orange.

The set of all added accurate values, is not itself an accurate value.

This proof is done under Standard Math.

 

[doronshadmi]

Um, no. It is an infinite series, and its value is X.

http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 .

 

[doronshadmi]

Perhaps you should actually read the references you cite. From the second sentence: Such proofs can be considered more elegant than...mathematically rigourous proofs

I say you are wrong; wikipedia says you are wrong. "Proof without words" are not rigorous proofs.

Simply wrong conclusion. Here is the whole text ( http://en.wikipedia.org/wiki/Proof_without_words ):

"In mathematics, a proof without words is a proof of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than more formal and mathematically rigourous proofs due to their self-evident nature."

So according the whole text, a proof without words is even better then formal proofs that are based only of strings of text and symbols.

"[1] When the diagram demonstrates a particular case of a general statement, to be a proof, it must be able to be generalised."

Indeed my proof without words, is related also to 0.1+0.01+0.001+...[base 2] ... < ... 0.9+0.09+0.009+...[base 10] ... < 1

 

[jsfisher]

So according the whole text, a proof without words is even better then formal proofs that are based only of strings of text and symbols.

Ah! So in doronetics, the lack of rigor makes something better than a formal proof.


Doesn't matter anyway, since your AutoCAD sketch isn't a proof of any sort, with or without words.

 

[jsfisher]

Let us use the terminology of Standard Math (including the term "all" about a given class), in order to demonstrate the failure of Standard Math within its own context, about the argument that the infinite convergent series (2a+2b+2c+2d+…) = X, where X is a constant and accurate value > 0.

It is obvious that any accurate value of the infinite convergent series (2a+2b+2c+2d+…)

An infinite series either has a value (i.e. it converges) or it doesn't. There's no sequence of values as you are implying. So, already you have failed to use "the terminology of Standard Math," and the assumes we'd overlook your "accurate value" nonsense.

Doron fail 1, Mathematics, 0.

...is the result of the projection of the different ends of any given bended form of the class of all bended forms of constant X>0 accurate value, upon the non-bended form of constant X>0.

Back to "bended", I see. There's a high gibberish quotient, here, too, and you are again trying to characterize an infinite series as a sequence. It is not.

Doron fail 2, Mathematics, 0.

Since any bended form of X has two different ends, then 2*0 is not one of the projections of the class of all bended forms of constant X>0 upon the non-bended form of constant X>0.

Are you now trying to say that the width of each of your Koch curve generations (which you denoted as Y before you ran away from a simple question) is greater than 0 for all generations? Another "bended", too.

Hard to count this as any additional doron fail, so the score remains unchanged.

As a result the two different ends are an essential property of both [the class of all bended forms of constant X>0 accurate value] AND [the infinite convergent series (2a+2b+2c+2d+…)

"Essential", eh? Interesting choice of words. What would have made the property non-essential? Be that as it may, the conclusion is faulty. The "class of all bended forms"[sic] is an infinite set, and an infinite series is a singleton.

Doron fail 3, Mathematics, 0.

...which is the result of the projection of the different ends of any given bended form of the class of all bended forms of constant X>0 accurate value, upon the non-bended form of constant X>0].

Maybe it is your notation that fails you. (Well, it's one of many things that fails you....) Let S₁ = 2a, and S₂ = 2a+2b, and S₃ = 2a+2b+2c, and so on. And let S = (2a+2b+2c+2d+...).

Are all these things you are trying to say about S really about the sequence S_i? Sure looks like it.

Doron fail 4, Mathematics, 0.

Conclusion: the result of the added accurate values of all projections that are derived from the class of all bended forms of constant X>0 upon the non-bended form of constant X>0, can't be but < constant X>0.

You can make the true statement that for all i, S_i < X. You cannot make the same statement about S, though. S is the limit of S_i as i approaches infinity, and as such S = X.

Doron fail 5, Mathematics, 0.

Doron, you didn't do so well with your demonstration. In fact, you proved the opposite of what you expected.

 

[doronshadmi]

Ah! So in doronetics, the lack of rigor makes something better than a formal proof.


Doesn't matter anyway, since your AutoCAD sketch isn't a proof of any sort, with or without words.

jsfisher http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 proof without words is an irresistible fact

In http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 version I use the term "all" and yet it is rigorously proved that (2a+2b+2c+2d+…) < X.

You simply can't do anything about this buautiful fact.

 

[jsfisher]

jsfisher http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 proof without words is an irresistible fact

More of a pipe dream on your part. See: http://www.internationalskeptics.com/forums/showpost.php?p=5786101&postcount=9269

In http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 version I use the term "all" and yet it is rigorously proved that (2a+2b+2c+2d+…) < X.

You keep using that word, rigorously, incorrectly. It doesn't mean fail. See: http://www.internationalskeptics.com/forums/showpost.php?p=5786101&postcount=9269

You simply can't do anything about this buautiful fact.

You haven't produced anything approaching a beautiful fact. See: http://www.internationalskeptics.com/forums/showpost.php?p=5786101&postcount=9269

 

[doronshadmi]

You can make the true statement that for all i, S_i < X. You cannot make the same statement about S, though. S is the limit of S_i as i approaches infinity, and as such S = X.

A load of crap.

(2a+2b+2c+2d+...) inaccurate value < X accurate value, so if S = X then (2a+2b+2c+2d+...) inaccurate value < S accurate value.

Your game with symbols has no impact on this fact, jsfisher.

An infinite series either has a value (i.e. it converges) or it doesn't.

An infinite series does not have an accurate value, which is a fact that your limited reasoning can't comprehend.

 

[jsfisher]

A load of crap.

(2a+2b+2c+2d+...) inaccurate value < X accurate value, so if S = X then (2a+2b+2c+2d+...) inaccurate value < S accurate value.

So you claim. Yet, you are unable to establish your claim by any means other than brute-force repetition.

The fact remains, the fact you cannot comprehend, is that infinite series are defined by the limits of their underlying infinite sequence. (2a+2b+2c+2d+...) is X, exactly, as a matter of definition.

You failures in comprehension do not constitute errors in Mathematics.

Your game with symbols has no impact on this fact, jsfisher.

It wasn't a "game of symbols". It was a question of series versus sequence. You are conflating the two. You clearly don't understand the difference. And you refuse to learn the difference.

You also don't appreciate the hypocritical irony in you statement, either, do you?

An infinite series does not have an accurate value, which is a fact that your limited reasoning can't comprehend.

Prove it.

By the way, when is Y = 0? Or will this be yet another of the long sequence of completely wrong statements made by doronshadmi from which doronshadmi runs and hides?

 

[doronshadmi]

The fact remains, the fact you cannot comprehend, is that infinite series are defined by the limits of their underlying infinite sequence. (2a+2b+2c+2d+...) is X, exactly, as a matter of definition.

Your "matter of definition" is nothing but a game with text and symbols, without any underlying of what you call "reasoning".

The order of (2a+2b+2c+2d+...) has no significance on the result, which is an inaccurate value < X.

Exactly the same thing can be shown about Aleph0 and 1+1+1+…

1+1+1+… inaccurate value < Aleph0 accurate value, and it is absolutely clear that each 1 of 1+1+1+… is mapped with some unique natural number, such that no natural number is missing.

Your "reasoning" about the infinite Complexity is a load of crap, jsfisher and I proved that it is a load of crap.

You play with finite collections and imagine that they are infinite collections, but this is only is your false dream, jsfisher.

Yet, you are unable to establish your claim by any means other than brute-force repetition.

The brute-force repetition is a exactly your false dream about infinite collections by forcing on them properties that are taken from finite collections, for example: your false claim that infinitely many positive added accurate (and finite) values have an accurate value.

In http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 it is proved (and this proof is done under Standard Math) that your "reasoning" does not hold water.

 

[doronshadmi]

Maybe it is your notation that fails you. (Well, it's one of many things that fails you....) Let S₁ = 2a, and S₂ = 2a+2b, and S₃ = 2a+2b+2c, and so on. And let S = (2a+2b+2c+2d+...).

Are all these things you are trying to say about S really about the sequence S_i? Sure looks like it

Only in your limited dream.

I am talking about exactly S_∞ = (2a+2b+2c+2d+...)

 

[jsfisher]

Your "matter of definition" is nothing but a game with text and symbols, without any underlying of what you call "reasoning".

Perhaps if you actually understood the definitions, you'd be less willing to ignore them. Still, they are what they are, and they are not subject you your arbitrary changes.

The order of (2a+2b+2c+2d+...) has no significance on the result, which is an inaccurate value < X.

Order can make a difference in a series, but not this one...and this result is exact.

Exactly the same thing can be shown about Aleph0 and 1+1+1+…

Exact what same thing? The series, 1+1+1+1+..., doesn't converge. What point are you trying to make, other than an additional display of your ignorance?

1+1+1+… inaccurate value < Aleph0 accurate value

No, on several counts. The series does not have a value, period. Aleph₀ doesn't have a value, either, at least not in a meaningful sense of the instant example. Values don't get categorized as accurate and inaccurate in real Mathematics, either.

...and it is absolutely clear that each 1 of 1+1+1+… is mapped with some unique natural number, such that no natural number is missing.

Not "is mapped". "Can be mapped" perhaps, but certainly not "is mapped". Must you muddle everything?

Your "reasoning" about the infinite Complexity is a load of crap, jsfisher and I proved that it is a load of crap.

"Complexity" is your undefined term, not mine. The load of crap regarding it is all yours, as well.

You play with finite collections and imagine that they are infinite collections, but this is only is your false dream, jsfisher.

When did I do that? Another doron lie, I see.

The brute-force repetition is a exactly your false dream about infinite collections

What does this non sequitur have do to with you repeating your claims without proof?

...by forcing on them properties that are taken from finite collections, for example: your false claim that infinitely many positive added accurate (and finite) values have an accurate value.

And yet, you cannot show any claim I have made to be false. You can only repeat them without evidence....just as I said: your brute-force repetition.

In http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 it is proved (and this proof is done under Standard Math) that your "reasoning" does not hold water.

Not quite. Your post is nonsense, as demonstrated in yet another post you run away from: http://www.internationalskeptics.com/forums/showpost.php?p=5786101&postcount=9269

 

[jsfisher]

Maybe it is your notation that fails you. (Well, it's one of many things that fails you....) Let S₁ = 2a, and S₂ = 2a+2b, and S₃ = 2a+2b+2c, and so on. And let S = (2a+2b+2c+2d+...).

Are all these things you are trying to say about S really about the sequence S_i? Sure looks like it

Only in your limited dream.

I am talking about exactly S_∞ = (2a+2b+2c+2d+...)

Too bad for you, then.

That only makes your posts sillier. First, even here you insist on changing the notation from what was already introduced -- what was that you said about dumb notation games? Second, you have confirmed that you really meant to give the infinite series S (or S_∞ if you insist) characteristics of a sequence, which it isn't.

At least you are consistent in being wrong.

 

[doronshadmi]

you have confirmed that you really meant to give the infinite series S (or S∞ if you insist) characteristics of a sequence, which it isn't.

S = (2b+2c+2a+2d+...) = (2a+2b+2c+2d+...) < X, whether you like it or not.

jsfisher, your limited notion can get things only in terms of accurate values.

As a result you are unable to comprehend my proof ( http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 ) about (2a+2b+2c+2d+...) < X.

 

[doronshadmi]

The series, 1+1+1+1+..., doesn't converge

It does not matter if it is converges or diverges , you simply have no ability to deal with inaccurate values because you do not understand the real nature of infinite collections, and this is exactly the reason for your failure.

 

[jsfisher]

S = (2b+2c+2a+2d+...) = (2a+2b+2c+2d+...) < X, whether you like it or not.

Only according to you. For those of us grounded in real Mathematics, we'll choose not to believe you.

jsfisher, your limited notion can get things only in terms of accurate values.

Yes, that would be the sane thing to do.

As a result you are unable to comprehend my proof.

For it to be a proof, it would, at the very least, have fewer errors.