Deeper than primes

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doronshadmi said:
It does not matter if it is converges or diverges
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There are other possibilities, you know. Oops, no, you probably don't know, do you?

...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.
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These are all things you have simply made up. Curiously, though, you cannot describe your imaginary friend in any detail, provide any operational definitions, nor even provide a realistic example of its utility.

Instead, you give us gibberish, contradiction, inconsistencies, and thorough misunderstanding of real math.


Face it. You don't like, don't understand that the valuation of an infinite series is defined in terms of limits.

The definition is part of real mathematics because it has utility. Don't like it? Tough. It's a definition, and it doesn't depend on your love and understanding.

Want to discredit it? Demonstrate a problem with it, and do so without a boat-load of erroneous statements about other parts of Mathematics you don't understand either.
 
jsfisher said:
Only according to you. For those of us grounded in real Mathematics, we'll choose not to believe you.
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Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.
 
jsfisher said:
Only according to you. For those of us grounded in real Mathematics, we'll choose not to believe you.
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Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.

Face it, Y (which is a variant) is the complement of S = (2a+2b+2c+2d+…) to X.

Since Y can't be 0 in real Math, then S-Y<X by Y>0, where both S and Y are inaccurate values > 0.

S-Y<X by Y>0 is an invariant mathematical fact, that can be clearly seen by the following proof without words, about the relations of S with Y, such that S-Y<X by Y>0:

4464201033_30e7dbd8d4_o.jpg


Since variable Y>0 then we get a polygon with at least 4 ends.

S = X only if this polygon has at most 3 end (it is a triangle).

Because variable Y>0, then this polygon has at least 4 ends, and S=X is false.

Y>0 = 0.000…1[base 2] in the case of S = (0.1+0.01+0.001+…) < 1.

…

Y>0 = 0.000…1[base 10] in the case of S = (0.9+0.09+0.009+…) < 1.

…

etc. ad infinitum.


Since by Standard Math S = (0.1+0.01+0.001+…) = 1, then the complement of S to X (which is Y) must be = 0.

So we see how Standard Math forces a triangle (at most 3 ends) on a polygon that has at least 4 ends.

Say no more.
 
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jsfisher said:
The definition is part of real mathematics because it has utility.
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Riemannian geometry definitions became utilities in Einstein's GRT about 40 years later.

The definitions of Galois theory became utilities in Modern Science about 100 years later.

So you have no case, jsfisher.
 
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doronshadmi said:
Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.
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More brute-force repetition from a prior post? This is not a valid proof method, despite your preference for it.

Face it, Y (which is a variant) is the complement of S = (2a+2b+2c+2d+…) to X.
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No, this is just wrong. You have muddled things, and in your muddle you make false statements.

Let's clean up the notation for starters. You had a construction for generations of Koch curve generations, and referred to two measures, length and width. You muddled all your measures together without regard to generation. Properly, we should be referring to length as Xn for Kn, the latter being the n-th generation Koch curve. Yn should be the width of Kn. We also have S and Sn that were introduced a few posts back (without muddle, because I introduced them, not your).

With this de-muddled nomenclature, what is clear is that, (1) for all n, Xn = a constant which we can call X, and (2) for all n, Yn = Xn - Sn.

Note that #2 is a difference relation, not complement.

Is there some part of this you dispute?

Since Y can't be 0 in real Math, then S-Y<X by Y>0, where both S and Y are inaccurate values > 0.
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See what I mean about muddle? Well, of course you don't, but others do. Let's de-muddle your statement:
For all n, Yn is > 0, therefore S - Yn < X.​

Odd you'd introduce this, doron. It relies on the fact you've been fighting, that S = X. You can't just accept a fact at one point then later reject it out of convenience, you know.

S-Y<X by Y>0 is an invariant mathematical fact, that can be clearly seen by the following proof without words, about the relations of S with Y, such that S-Y<X by Y>0

http://farm3.static.flickr.com/2794/4464201033_30e7dbd8d4_o.jpg
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De-muddled:
For all n, S - Yn < X. The following is an AutoCAD sketch with which I just love to spam this thread, because I can use it to further muddle an already muddled discussion.​

Note the repetition of the already made point, that S - Yn < X. I'm not sure what the purpose that served.

Since variable Y>0 then we get a polygon with at least 4 ends.

S = X only if this polygon has at most 3 end (it is a triangle).

Because variable Y>0, then this polygon has at least 4 ends, and S=X is false.
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Hmm. No point de-muddling this. It has been overrun with gibberish and nonsense. Polygon with 4 ends? What polygon? What ends?

It seems as if you are trying to make a huge leap from Sn to S. Your muddle, gibberish, and nonsense do not span that gap for you.
 
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doronshadmi said:
Riemannian geometry definitions became utilities in Einstein's GRT about 40 years later.

The definitions of Galois theory became utilities in Modern Science about 100 years later.
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Wow! Do you know what this does to improve your Crank index? Well done!

That aside, your reply is a non sequitur. Care to try again?
 
doronshadmi said:
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.
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A circle does not have “two different ends”. So your assertion fails with a very simple and basic example.

You asserted that you would “use the terminology of Standard Math”. Where do you find this “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” gibberish as part of that?


doronshadmi said:
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.
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As your “obvious” assumption is obviously wrong (as demonstrated by a circle) your “conclusion” based on the gibberish assumption is equally erroneous and gibberish. Simply put, a constant is, well, constant. None of your nonsensical gibberish or clearly wrong “obvious” assumptions can change or are needed to support that simple fact.

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

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]
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The only “proof” seen there is that you simply don’t understand what a proof or rigorous means.


doronshadmi said:
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.
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By all means please show your “unclosed gap” in an infinite and convergent series. Doron you still don’t understand that adding zero to the series adds, well, zero to the series. If adding zero closes your “unclosed gap” then there was no gap to close.

doronshadmi said:
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).
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What "We" are you referring to? You and your imagination? Again that an infinite convergent series has a finite and accurate sum was proven some 2,300 years ago.


doronshadmi said:
The set of all oranges is not itself and orange.
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Because a set is a set not, well, an orange.

doronshadmi said:
The set of all added accurate values, is not itself an accurate value.
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Because a set is a set not, well, a value, though such a set can have a sum which would be a value and not, well, a set.

doronshadmi said:
This proof is done under Standard Math.
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Clearly not, as none of your nonsensical gibberish is consistent with what you like to call “Standard Math”.
 
doronshadmi said:
Here:
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Again where did anyone claim you drew a circle in your diagram? Nowhere in that quote, or that post that it is from, do I claim you drew a circle in your diagram. In fact the basic assertion of that quote is that you are simply ignoring a circle (among other geometric shapes) in your claim that “any bended form of X has two different ends”. If you simply meant to say that considering only the “bended form of X” shown in your diagram then “X” “has two different ends” then you should have been more specific. However then that would simply contradict your claim of using “the terminology of Standard Math (including the term "all" about a given class)”. So either you were talking about “any bended form of X” (meaning all “bended” forms “of X”) or you were just talking about a very specific “bended form of X” as in your diagram. Either way none of this helps you with the fact that adding zero to the series still adds, well, zero to the series.
 
doronshadmi said:
jsfisher said:
Polygon with 4 ends? What polygon? What ends?
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http://farm5.static.flickr.com/4063/4490940378_b65cb4c07f_o.jpg
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Didn't understand the question, did you? Polygons, being closed curves, don't have ends.

As you see in the first diagram, jsfisher, variable Y>0 is the complement of S to X.
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First, nowhere in your AutoCAD masterpiece does a variable Y appear, so you claim is bogus before the gates even open. Second, you've completely failed to provide any generational reference. We all know you prefer to leave things as confused as possible so you can make these false leaps in illogic, but it is kind of important. Third, complement continues to be an unacceptable word in this context. It's that subtraction thing...a value minus a value is a difference, not a complement.

Why must you muddle so? I'm sure if you try really, really hard you can make a correct statement about you Koch curve generation thingy.
 
The Man said:
Again where did anyone claim you drew a circle in your diagram? Nowhere in that quote, or that post that it is from, do I claim you drew a circle in your diagram. In fact the basic assertion of that quote is that you are simply ignoring a circle (among other geometric shapes) in your claim that “any bended form of X has two different ends”. If you simply meant to say that considering only the “bended form of X” shown in your diagram then “X” “has two different ends” then you should have been more specific. However then that would simply contradict your claim of using “the terminology of Standard Math (including the term "all" about a given class)”. So either you were talking about “any bended form of X” (meaning all “bended” forms “of X”) or you were just talking about a very specific “bended form of X” as in your diagram. Either way none of this helps you with the fact that adding zero to the series still adds, well, zero to the series.
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The Man, I am talking exactly about the class of the projections of the different ends of all bended forms of constant X>0 upon the non-bended form of constant X>0.

Your reply to post http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 is simply irrelevant.
 
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doronshadmi said:
Didn't understand the answer, did you jsfisher?

Ask some child, maybe he will help you.
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All the children I know know the difference between ends and edges. It saddens me to know, though, that your schools in Israel are worse than those here.

They also don't say "bended" when they mean "bent". So many, many things the children I know get right.
 
jsfisher said:
All the children I know know the difference between ends and edges. It saddens me to know, though, that your schools in Israel are worse than those here.

They also don't say "bended" when they mean "bent". So many, many things the children I know get right.
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jsfisher, call it end, call it edge, call it $%&^$.

It does not change my argument about polygons with 4 endpoints or 3 endpoints,
and their relevancy to Y as a complement of S to X.

Once again it is demonstrated how limited are your abstraction abilities, exactly because you have no ability to generalize your reasoning beyond any particular representation of it.
 
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doronshadmi said:
The Man, I am talking exactly about the class of the projections of the different ends of all bended forms of constant X>0 upon the non-bended form of constant X>0.

Your reply to post http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265 is simply irrelevant.
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Again a circle is a "bended" form "of constant X>0" that does not have "ends". So you are not talking about " all bended forms of constant X>0" just some with "ends". Your response above as well as your

doronshadmi said:
...post http://www.internationalskeptics.com/forums/showpost.php?p=5785618&postcount=9265...
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remain simply irrelevant. As again adding zero to the series still only adds zero to the series and a constant is just that, constant. That you think adding zero is somehow required for or part of the convergent series and that anyone (but you) would claim that a constant which is specified as being greater than zero somehow equals zero, simply demonstrates that you in fact have absolutely no idea what you are talking about.
 
doronshadmi said:
jsfisher, call it end, call it edge, call it $%&^$.
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Since you are offering to be flexible in this, how about we just call things by there proper names? Novel concept for you, I know, but why not give it a try?

It does not change my argument about polygons with 4 endpoints or 3 endpoints
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No, does not change your argument at all. Polygons don't have endpoints, be it 3 or 4, so your argument is completely wrong.
,
...and their relevancy to Y as a complement of S to X.
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And this part is unchanged, too. Completely wrong for the reasons already given.

Once again it is demonstrated how limited are your abstraction abilities, exactly because you have no ability to generalize your reasoning beyond any particular representation of it.
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Actually, you are doing all the demonstrating -- of how muddle, gibberish, contradiction, inconsistency, and illogic produce fail in so many different variations.


What was all this tangent of fail for? Oh, yeah. You still cannot understand how an infinite series can have an exact value. All this nonsense just to give yourself some comfort in your denial.

Doesn't matter, though. Real Mathematics continues along just fine, highly useful and no apparent inconsistencies that can't be managed. Doronetics, on the other hand, is still stuck at zero.
 
The Man said:
Again a circle is a "bended" form "of constant X>0" that does not have "ends".
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And it is irrelevant to the class of all the projections of the different ends of all bended forms of constant X>0 upon the non-bended form of constant X>0, exactly as it is defined by:

4430320710_daf5b36c0f_o.jpg


The Man I see that you wish to become an expert of irreverent replies.
 
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The Man said:
remain simply irrelevant. As again adding zero to the series still only adds zero to the series and a constant is just that, constant. That you think adding zero is somehow required for or part of the convergent series and that anyone (but you) would claim that a constant which is specified as being greater than zero somehow equals zero, simply demonstrates that you in fact have absolutely no idea what you are talking about.
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http://www.internationalskeptics.com/forums/showpost.php?p=5791966&postcount=9304.
 
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EDIT:

jsfisher said:
You still cannot understand how an infinite series can have an exact value.
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The Man said:
As again adding zero to the series still only adds zero to the series and a constant is just that, constant. That you think adding zero is somehow required for or part of the convergent series and that anyone (but you) would claim that a constant which is specified as being greater than zero somehow equals zero, simply demonstrates that you in fact have absolutely no idea what you are talking about.
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Again 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 (the variant Y>0, which is the complement of S to X) between the class of all bended Koch's fractal forms of constant X>0 accurate value, and its projection ( which is exactly the infinite convergent series S=(2a+2b+2c+2d+…) ) upon the non-bended form of the constant and accurate value X>0.

jsfisher and The Man,

You still cannot understand how an infinite series has an inaccurate value, exactly because variant Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is > 0, exactly as shown by the red non-triangle polygon:

4490940378_b65cb4c07f_o.jpg


By your wrong reasoning Y=0 (the red triangle polygon), and you are unable to grasp that if Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is = 0, then it has no impact on the result (exactly as The Man said), so only the complement variant Y>0 is relevant, and as a result S = (2a+2b+2c+2d+...) < X by variant Y>0(exactly as shown by the red non-triangle polygon, where the red non-triangle polygon, is an invariant form).

Both S AND Y are inaccurate values > 0, which is a fact that your Limit-oriented reasoning can't comprehend.
 
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doronshadmi said:
Again 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 (the variant Y>0, which is the complement of S to X) between the class of all bended Koch's fractal 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.
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Once again, show your “unclosed gap” in the infinite convergent series.




doronshadmi said:
jsfisher and The Man,

You still cannot understand how an infinite series has an inaccurate value, exactly because variant Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is > 0, exactly as shown by the red non-triangle polygon:


[qimg]http://farm5.static.flickr.com/4063/4490940378_b65cb4c07f_o.jpg[/qimg]
Click to expand...


Doron you simply can not understand that your “red non-triangle polygon” is the result of a finite number of iterations.

doronshadmi said:
By your idiotic reasoning Y=0 (the red triangle polygon), and you are unable to grasp that if Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is = 0, then it has no impact on the result (exactly as The Man said), so only the complement invariant Y>0 is relevant, and as a result S = (2a+2b+2c+2d+...) < X (exactly as shown by the red non-triangle polygon).
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“exactly as The Man said” was that adding zero to a sum has zero impact on that sum. Certainly as I have been repeatedly saying that and have finally gotten you to at least agree with that, I was, and am, indeed able to grasp that. Although I don’t think you fully grasp it yet. As jsfisher has asked you several times

jsfisher said:
So, when is Y = 0, as you claimed it?
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doronshadmi said:
Again 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
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You say that like it means something special. It doesn't, and you are unable to show otherwise. You continue to ignore / misunderstand / abuse / corrupt what is meant by an infinite series, such as S.

S has a fixed, well-defined, finite value. It is exactly equal to the limit of Sq as q approaches infinity. That's a matter of definition.


...(the variant Y>0, which is the complement of S to X)
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Difference. Please try to get at least one thing right.

...between the class of all bended
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Bent. You just try to hard to be wrong all the time.

...Koch's fractal forms of constant X>0 accurate value, and its projection ( which is exactly the infinite convergent series S=(2a+2b+2c+2d+…) ) upon the non-bended form of the constant and accurate value X>0.
Click to expand...

My, isn't that a muddle. You could have just said "width" and avoided all that gibberish.

jsfisher and The Man,

You still cannot understand how an infinite series has an inaccurate value
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No, we understand infinite series just fine. It is you that doesn't understand them, or much else mathematical. You insist things are defined differently than they are and behave differently than they do.

...exactly because variant Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is > 0, exactly as shown by the red non-triangle polygon
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More muddle. No, Y = 0. On the other hand, Yi > 0 for all i. You really should try to keep these things straight. And it is still not the complement. It's a difference relationship.

http://farm5.static.flickr.com/4063/4490940378_b65cb4c07f_o.jpg

By your wrong reasoning Y=0 (the red triangle polygon), and you are unable to grasp that if Y (which is the complement of S = (2a+2b+2c+2d+...) to X) is = 0, then it has no impact on the result (exactly as The Man said), so only the complement variant Y>0 is relevant, and as a result S = (2a+2b+2c+2d+...) < X by variant Y>0(exactly as shown by the red non-triangle polygon, where the red non-triangle polygon, is an invariant form).
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More muddle. More gibberish. Yes, Y = 0 (no, not the red triangle). Y is the limit of Yi as i approaches infinity. Yi is the width of Ki, the i-th generation of Koch's curve. Yi = X - Si, a difference relationship. Finally, Y = X - S = 0.

All of these are consistent results within Mathematics. However, since you fog everything with misuse and muddle, it is no surprise you get so many things all wrong.

Both S AND Y are inaccurate values > 0, which is a fact that your Limit-oriented reasoning can't comprehend.
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You repeat this claim often, yet you cannot support it.
 
EDIT:

The Man said:
Doron you simply can not understand that your “red non-triangle polygon” is the result of a finite number of iterations.
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No The Man,

You simply can't understand that variant Y>0 is a complement of S=(2a+2b+2c+2d+...) upon infinitely many bended levels, where S is an inaccurate result of infinitely many accurate values.

The set of all oranges is not itself an orange.

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

My Koch's proof is done under Standard Math.

The Man said:
“exactly as The Man said” was that adding zero to a sum has zero impact on that sum. Certainly as I have been repeatedly saying that and have finally gotten you to at least agree with that, I was, and am, indeed able to grasp that.
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Once again, your limited reasoning (already shown in http://www.internationalskeptics.com/forums/showpost.php?p=5735873&postcount=9169) deals only with accurate (fixed) values, and it is based on local-only view of the researched subject.

The Man said:
Once again, show your “unclosed gap” in the infinite convergent series.
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No problem:

0.1+0.01+0.001+...[base 2] < 1 by 0.000…1[base 2], where both 0.1+0.01+0.001+...[base 2] and 0.000…1[base 2] are inaccurate values.

…

0.9+0.09+0.009+...[base 10] < 1 by 0.000…1[base 10], where both 0.9+0.09+0.009+...[base 10] and 0.000…1[base 10] are inaccurate values.

...

etc. … ad infinituum.
 
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EDIT:

jsfisher said:
You really should try to keep these things straight. And it is still not the complement. It's a difference relationship.
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No jsfisher, variant Y > 0 is the inaccurate value that complements S=(2a+2b+2c+2d+...) inaccurate value to X accurate value.
jsfisher said:
You say that like it means something special. It doesn't, and you are unable to show otherwise. You continue to ignore / misunderstand / abuse / corrupt what is meant by an infinite series, such as S.
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Your limited reasoning and the definitions that are derived form this limited reasoning, simply can't comprehend the real nature of infinite collections (where an infinite series is some particular case of an infinite collection).
jsfisher said:
Finally, Y = X - S = 0.
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So now Y=0, so what happend to
jsfisher said:
For instance, when is Y ever 0? [Hint: Never.] (http://www.internationalskeptics.com/forums/showpost.php?p=5761323&postcount=9224)
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, jsfisher?

According to you jsfisher: Finally an infinite series has a finite value. And you, jsfisher, dare to claim that you do not force the finite on the infinite.

jsfisher said:
All of these are consistent results within Mathematics.
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Some correction: All of these are inconsistent results within Mathematics.
 
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jsfisher said:
Yes, Y = 0 (no, not the red triangle). …. Finally, Y = X - S = 0
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Let us see:
4490940378_b65cb4c07f_o.jpg


Well, jsfisher, you have failed. Y=0 is exactly the red triangle.
 
doronshadmi said:
No The Man,

You simply can't understand that Y>0 is a complement of S=(2a+2b+2c+2d+...), where S is an inaccurate result of infinitely many accurate values.
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No Doron “S” is just a sum (in this case the sum of a convergent infinite series) and has nothing to do with your “inaccurate” fantasies.


doronshadmi said:
The set of all oranges is not itself an orange.

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

My Koch's proof is done under Standard Math.
Click to expand...



The Man said:
doronshadmi said:
The set of all oranges is not itself and orange.
Click to expand...

Because a set is a set not, well, an orange.

doronshadmi said:
The set of all added accurate values, is not itself an accurate value.
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Because a set is a set not, well, a value, though such a set can have a sum which would be a value and not, well, a set.

doronshadmi said:
This proof is done under Standard Math.
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Clearly not, as none of your nonsensical gibberish is consistent with what you like to call “Standard Math”.
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Repeating your nonsensical gibberish that has already been addressed Doron does not make it any less nonsensical gibberish having already been addressed.

doronshadmi said:
Once again, your limited reasoning (already shown in http://www.internationalskeptics.com/forums/showpost.php...postcount=9169) deals only with accurate (fixed) values, and it is based on local-only view of the researched subject.
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As I did not write that post or the paper you cite in that post, I do not see how you think that post applies to me. Other than the fact that you typically misinterpret what you read, like in that paper you cite, and as usual for you, you just like to attribute your misinterpretations to someone else. Particularly as I have already explained to you that math deals quite well variables (values that are not fixed) as well as estimated values, rages of values and rounded values (values that are not accurate). Once again you might have a better understanding of math and what terms like accurate mean if you had ever actually used math for anything other than just your fantasies.


doronshadmi said:
No problem:

0.1+0.01+0.001+...[base 2] < 1 by 0.000…1[base 2], where both 0.1+0.01+0.001+...[base 2] and 0.000…1[base 2] are inaccurate values.

…

0.9+0.09+0.009+...[base 10] < 1 by 0.000…1[base 10], where both 0.9+0.09+0.009+...[base 10] and 0.000…1[base 10] are inaccurate values.

...

etc. … ad infinituum.
Click to expand...


Obviously you’ve still got that problem of you thinking that because you claim there is an “uncovered gap” and give it some nonsensical representation like “0.000…1[base 2]” somehow shows that there is an “uncovered gap”.

None of your assumptions, misinterpretations, contrivances or drawings will change the fact that the difference between the series ½+1/4+1/8+1/16…. and the self similar two times series 1+½+1/4+1/8+1/16… is just 1 (an “accurate value” by your own assertions) which is itself the sum of the series ½+1/4+1/8+1/16…. by that same two times self similar relationship. That is all anyone needs to show that you are just completely and utterly wrong about the sum of a convergent infinite series even some 2,300 yea
 
doronshadmi said:
jsfisher, call it end, call it edge, call it $%&^$.

It does not change my argument about polygons with 4 endpoints or 3 endpoints,
and their relevancy to Y as a complement of S to X.

Once again it is demonstrated how limited are your abstraction abilities, exactly because you have no ability to generalize your reasoning beyond any particular representation of it.
Click to expand...

Does it ever enter your head that you might actually be wrong about something? We all make mistakes sometimes.
 
doronshadmi said:
EDIT:

jsfisher said:
You really should try to keep these things straight. And it is still not the complement. It's a difference relationship.
Click to expand...
No jsfisher, variant Y > 0 is the inaccurate value that complements S=(2a+2b+2c+2d+...) inaccurate value to X accurate value.
Click to expand...

You still insist on muddle, I see. Which Y is that? I've been very clear what my Yi terms are. And I have been equally clear that my use of the lone Y is the limit of Yi as i approaches infinity. You on the other hand, just insist on muddle.

You also insist on using the wrong terms. You aren't very good at this math thing at all, doron.

jsfisher said:
You say that like it means something special. It doesn't, and you are unable to show otherwise. You continue to ignore / misunderstand / abuse / corrupt what is meant by an infinite series, such as S.
Click to expand...

Your limited reasoning and the definitions that are derived form this limited reasoning, simply can't comprehend the real nature of infinite collections (where an infinite series is some particular case of an infinite collection).
Click to expand...

Umm, no. You are the one that claimed to be working within the bounds of "standard math". In point of fact you continue to get that all very wrong, but still, you claimed "standard math" as the domain for the discussion. Don't blame me just because you can't cope with the very domain upon which you insisted.

jsfisher said:
Finally, Y = X - S = 0.
Click to expand...
So now Y=0, so what happend to
jsfisher said:
For instance, when is Y ever 0? [Hint: Never.] (http://www.internationalskeptics.com/forums/showpost.php?p=5761323&postcount=9224)
Click to expand...
, jsfisher?
Click to expand...

You aren't paying attention, are you? I have been very clear in my usage of X, Y, and S, with and without qualifying subscripts. Your Y, on the other hand, has been one continuous muddle of Ysomething, but you are always, deliberately unclear about what the something is. Your Y is never 0, even though you claimed "by standard math" it was. My Y, on the other hand, is always 0.

According to you jsfisher: Finally an infinite series has a finite value. And you, jsfisher, dare to claim that you do not force the finite on the infinite.
Click to expand...

Nothing was forced. No numbers were injured producing an infinite summation.

jsfisher said:
All of these are consistent results within Mathematics.
Click to expand...

Some correction: All of these are inconsistent results within Mathematics.
Click to expand...

Prove it.

And, please, without all the blunders you have so far tried to pass off as proof.
 
The Man said:
No Doron “S” is just a sum (in this case the sum of a convergent infinite series) and has nothing to do with your “inaccurate” fantasies.
Click to expand...
No The Man “S” is just a fog (in this case the fog of a convergent infinite series) and has nothing to do with your “accurate” fantasies.

Look at this:

S=(0.9+0.09+0.09+0.009+...[base 10]) and it is a fog < 1 by fog 0.000...1[base 10]

As you see, all infinitely many added sums of the form above are not resulted by a sum, but they are resulted by a fog.

Exactly the same result it true for all infinitely many finite bended Koch’s fractal forms that have constant sum X AND different endpoints, where
S=(2a+2b+2c+2d+...) is exactly the projection of all these different endpoints upon the non-bended constant sum X.

Since all projections are the result of all bended Koch’s fractal forms that have constant sum X AND different endpoints, then the two different points are an invariant property of this projection, exactly because they belong to all infinitely many finite bended Koch’s fractal forms that have constant sum X, that can’t be reduced to sum 0.

As a result the sum of S < the constant sum X.

This result is clearly seen by this proof without words:

4430320710_daf5b36c0f_o.jpg
 
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jsfisher said:
You still insist on muddle, I see. Which Y is that? I've been very clear what my Yi terms are. And I have been equally clear that my use of the lone Y is the limit of Yi as i approaches infinity. You on the other hand, just insist on muddle.
Click to expand...
You still insist on irrelevant replies, because my argument is about not less than Y∞

Variant Y>0 exactly because S=(2a+2b+2c+2d+...) is the result of the invariant state of the projections of different endpoints of all bended Koch’s fractal forms that have constant sum X upon the non-bended constant sum X.

Your Y=0 is permanently out of the picture exactly because no bended Koch's fractal form is missing from the collection of all infinitely many finite bended Koch’s fractal forms that have constant sum X.
 
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jsfisher said:
You also insist on using the wrong terms. You aren't very good at this math thing at all, doron.
Click to expand...
I use Difference relationship between sums.

I use Complement relationship between fogs ( http://www.internationalskeptics.com/forums/showpost.php?p=5734631&postcount=9165 ).

EDIT:

Some correction of http://www.internationalskeptics.com/forums/showpost.php?p=5795158&postcount=9314.

Instead of “As a result the sum of S < the constant sum X” it has to be “As a result the fog of S < the constant sum X”.
 
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doronshadmi said:
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.
Click to expand...

The Man said:
Once again exactly wrong, Y is a variable not a value. It represents a range of values and you have asserted that …
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.
Click to expand...
ranges of values that have sums “can’t be but accurate values”. A convergent series is a range of values that has a sum. So by your own assertions it “can’t be but accurate values”. Again you claims are simply based on your assumption that an infinite convergent series has no sum, which was proven wrong some 2,300 years ago
Click to expand...
Anything that has a sum (range or not) is a finite (fixed) mathematical object.

Anything that has a fog (range or not) is an infinite (non-fixed) mathematical object.

The Man you simply unable to comprehend http://www.internationalskeptics.com/forums/showpost.php?p=5735873&postcount=9169 because of your "fixed-only" reasoning.

The Man said:
A convergent series is a range of values that has a sum.
Click to expand...

No, a convergent series is a range of values that has a fog.
 
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doronshadmi said:
....by fog 0.000...1[base 10] ....
Click to expand...

You do realize that "0.000......1" does not exist, do you? (who am I fooling, you probably do not and will refuse to accept this).

"...." means repeat indefinitely. How do you place a "1" after an indefinite number of "0"?
 
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sympathic said:
You do realize that "0.000......1" does not exist, do you? (who am I fooling, you probably do not and will refuse to accept this).

"...." means repeat indefinitely. How do you place a "1" after an indefinite number of "0"?
Click to expand...

EDIT:

"...1" of "0.000...1" represents (for example) the non-local unclosed gap between the infinite convergent series 0.9+0.09+0.009+...[base 10] and the natural number 1.

You can't get that because you can't comprehend the non-local atomic aspect, that can't be reduced to 0 (the local atomic aspect) by an infinite convergent series like 0.9+0.09+0.009+...[base 10], for example.

0.000...1 is a non-local number, also known as fog.
 
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doronshadmi said:
"...1" of "0.000...1" represents (for example) the non-local unclosed gap between the infinite convergent series 0.9+0.09+0.009+...[base 10] and the natural number 1.

You can't get that because you can't comprehend the non-local atomic aspect.
Click to expand...

1 / 3 * 3 = 1

regardless of which base you represent it in.
 
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