Deeper than primes

[jsfisher]

It does not matter if it is converges or diverges

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.

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.

 

[doronshadmi]

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

Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.

 

[dafydd]

Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.

How can you comment on real maths when you know nothing about it?

 

[doronshadmi]

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

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:

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.

 

[doronshadmi]

The definition is part of real mathematics because it has utility.

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.

 

[jsfisher]

Your "real" Mathematics is based on finite framework that is forced on infinite framework.

There is no room for beliefs in real Mathematics.

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.

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 X_n for K_n, the latter being the n-th generation Koch curve. Y_n should be the width of K_n. We also have S and S_n 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, X_n = a constant which we can call X, and (2) for all n, Y_n = X_n - S_n.

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.

See what I mean about muddle? Well, of course you don't, but others do. Let's de-muddle your statement:

For all n, Y_n is > 0, therefore S - Y_n < 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

De-muddled:

For all n, S - Y_n < 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 - Y_n < 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.

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 S_n to S. Your muddle, gibberish, and nonsense do not span that gap for you.

 

[jsfisher]

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.

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?

 

[The Man]

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.

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?

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.

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.

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

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

The only “proof” seen there is that you simply don’t understand what a proof or rigorous means.

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.

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.

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).

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.

The set of all oranges is not itself and orange.

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

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

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.

This proof is done under Standard Math.

Clearly not, as none of your nonsensical gibberish is consistent with what you like to call “Standard Math”.

 

[doronshadmi]

A circle does not have “two different ends”. So your assertion fails with a very simple and basic example.

Please show us the circle in:

 

[The Man]

Please show us the circle in:

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

Please show us where anyone claimed you drew a circle in your diagram.

 

[doronshadmi]

Polygon with 4 ends? What polygon? What ends?

As you see in the first diagram, jsfisher, variable Y>0 is the complement of S to X.

 

[doronshadmi]

Please show us where anyone claimed you drew a circle in your diagram.

Here:

A circle does not have “two different ends”.

 

[jsfisher]

Please show us where anyone claimed you drew a circle in your diagram.

Here:

A circle does not have “two different ends”.

Now, where, exactly, did The Man say that you drew a circle in your diagram? Is your reading comprehension really this bad?

 

[The Man]

Here:

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.

 

[jsfisher]

Polygon with 4 ends? What polygon? What ends?

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

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.

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.

 

[doronshadmi]

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.

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.

 

[doronshadmi]

Didn't understand the question, did you? Polygons, being closed curves, don't have ends.

Didn't understand the answer in http://www.internationalskeptics.com/forums/showpost.php?p=5790103&postcount=9291 about (the red) polygons with 4 or 3 ends, did you jsfisher?

Ask some child, maybe he will help you.

 

[jsfisher]

Didn't understand the answer, did you jsfisher?

Ask some child, maybe he will help you.

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.

 

[doronshadmi]

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, 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.

 

[The Man]

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.

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

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

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.