You seem to have avoided this question:
Now, exactly what has ever been accomplished with OM?
Deeper than primes
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Now, exactly what has ever been accomplished with OM?
doronshadmi
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You do not get the answer.
As for the technology that enables computers, it is used now to accelerate the built-in dichotomy between Ethics and Logics, which can easily resulted by our self destruction in the near future, unless we develop the technology of the consciousness, where both Ethics AND Logics are complements of a one complex and inherently incomplete (and therefore naturally opened) reasoning, that its L value of Drake's equation (http://en.wikipedia.org/wiki/Drake_equation) is undefined.
The Man
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Are you claiming X+X-X=X is invalid then?
Again your simple assumption that either of those series is “incomplete” does not make them incomplete. Nor do your futile attempts to simply make the word incomplete synonymous with infinite.
Again a circle, as a closed curve, is complete (it returns onto itself) so your use of circles (as does your insistence on closed curves) actually belies your assumption that they are incomplete.
I never claimed you used the phrase “last segment” in that or any other post.
So again…
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The Man
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Again, do you even understand what the "L value of Drake's equation" represents?
Well I certainly have to grant you that "inherently incomplete <snip> reasoning" accurately describes your methods.
doronshadmi
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The Man,
By trying to understand your view about my reasoning I find this:
You think that I interpret a converges geometric series like 1/2+1/4+1/8+… by using notions that are based on finite models.
You are wrong because a finite series like 1/2+1/4+1/8+ does not converge if it reaches a given limit (there are at least two segments of the same size in order to reach the value of the limit, but then the series does not converge, but simply reaches the value of the limit).
So we can't use a finite model when we deal with real convergence, where no two values of the same size are found in a series
like 1/2+1/4+1/8+ …
As a result real convergence is under the invariant state of being smaller, and this invariant property can't be found among any finite series.
The invariant state of being smaller is exactly the properly of real convergence and real convergence is expressed by an infinite series that can't reach a given limit (smaller means approaches, and no more than that).
By trying to understand your view about my reasoning I find this:
You think that I interpret a converges geometric series like 1/2+1/4+1/8+… by using notions that are based on finite models.
You are wrong because a finite series like 1/2+1/4+1/8+ does not converge if it reaches a given limit (there are at least two segments of the same size in order to reach the value of the limit, but then the series does not converge, but simply reaches the value of the limit).
So we can't use a finite model when we deal with real convergence, where no two values of the same size are found in a series
like 1/2+1/4+1/8+ …
As a result real convergence is under the invariant state of being smaller, and this invariant property can't be found among any finite series.
The invariant state of being smaller is exactly the properly of real convergence and real convergence is expressed by an infinite series that can't reach a given limit (smaller means approaches, and no more than that).
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doronshadmi
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http://en.wikipedia.org/wiki/Drake_equation
One of the reasons that L has a final value, is self destruction.
doronshadmi
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No, I claim that X is incomplete if it is a series of the form 1/2+1/4+1/8+... or 1/1+1/2+1/4+...
It is not an assumption, it is an axiom that your reasoning can't get, because your reasoning is limited to the concept of Collection.
No, a circle is complete only if it has no points along it.
Really?
Try this:
The Man said:
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jsfisher
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So you keep saying, and in so doing you continue to evade the question. You said that by standard mathematics...(0 = 1). You lied when you said that. It was by your own misunderstanding that you came to that bogus conclusion and then blamed everyone else for your failing.
By the way, since you don't care for Cantor's formulation, what would you like ∞*0 and ∞/∞ to be?
Yes, we should probably add:
"proof by direct perception"
to the list. Doron: if you can't dance don't blame the floor.
The Man
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From the article you linked
Doron there are plenty of reasons why a civilization may no longer “release detectable signals into space” or have never released “detectable signals into space” having nothing to do with “self destruction”. What is this morbid fixation you seem to have with our civilization and its “self destruction”? If you think your OM will stop the self destruction of our civilization then just say so, directly, but the “L” value in the Drake equation does not relate directly to self destruction, much as you might seem to enjoy thinking that it does.
The Man
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Again a claim that has been proven to be wrong some 2,300 years ago. Again your simple claim that those series are “incomplete” does not make them incomplete.
Just what do you think an axiom is other then something one assumes to be valid since it can not be proven or disproven within the given framework? Your “axiom” is just easily proven false for a convergent infinite series. You want to base you notion on false assumptions, that’s your problem.
Yes Doron we all know and understand you want them, so desperately, to be “incomplete” for your notions and will go to any length, including changing the meaning of complete so it just means finite. Again it just goes to show how blindly desperate you are to support your morbid fantasy of saving our civilization from its own self destruction.
Since you were unable to define your “closed curve” without points as you claimed you could, I doubt you will fare any better defining a circle without points. Again trying to make your “complete” synonymous with “no points” only goes to show how entirely contrived, self serving, superfluous and useless is your notion of “complete”.
That certainly does not claim that you used the phrase “last segment” but simple labels the concept you were expounding as “your concept of a ‘last segment’”. Perhaps it is the use of single ‘ ‘ vs. the double “ “ quotation marks that is confusing you “ “ would indicate a quotation, if I was quoting you or some one else directly, ‘ ‘ would tend to indicate some particular and potentially obscure use of a term or phrase that perhaps is not directly quoted for some one. A convention I have used numerous times on this thread when dealing with your rather unique usages of words and phrases. “ “ indicating a direct quote of your usage and ‘ ‘ indicating my own paraphrasing of terms to fit within your typical usage. I can understand how you might have been confused, but since I have pointed out to you specifically again that I was not quoting you or claiming that you ever used that particular phrase, your continued insistence of such is just your problem.
Reflection much?
doronshadmi
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No The Man, it was not proven to be wrong some 2,300 years ago, exactly because Non-locality was not understood by Archimedes.
X+X-X=X does not say anything about the difference between the finite (that reaches the limit) and the infinite (that approaches the limit at its best).
I see that you have missed http://www.internationalskeptics.com/forums/showpost.php?p=5675046&postcount=8885
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Poor old Archimedes. Lucky for him JREF did not exist back then so he could not have been told he just did not get it.
No, I suspect he was politely ignoring it.
doronshadmi
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Question: Just what you think is the reason of your limitation to get completeness in terms of a pointless circle?The Man said:
Answer: your inability to get things that are not Collections.
The Man said:
Wrong.
At the moment that you understand a pointless circle, then and only then you can easily understand that this completeness is the base ground for accurate values (which are finite) or inaccurate values (which are infinite).
A pointless circle is totally complete because is has no beginning AND no end (it has an atomic quality).
A circle with a single point along it defines a segment, and a closed segment is less complete than a pointless circle (completeness is a matter of Quality and not a matter of Quantity).
When more and more segments are used in order to define a circle, it becomes less and less complete, but as long as the amount of segments is finite, their added values have an accurate result known as Sum.
If an infinite amount of segments is used in order to define a circle, then also the accuracy of the result is lost and we do not have a Sum.
The best result of this inherent incompleteness is defined by an invariant proportion, which is possible exactly because at real convergence no two values of the same size are found in a series like 1/2+1/4+1/8+ … and this is an axiomatic fact that your limited reasoning simply can’t grasp.
Again it is shown why OM’s reasoning of EEM ( http://www.scribd.com/doc/16547236/EEM ) is desperately needed exactly because of blind and dogmatic scholars like you.The Man said:
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Oh, dear, here we go again. You're parading your ignorance for all to see, Doron.
How do you define a circle without using any points? Go on, please define a circle; how big is it, and where is it? How do you avoid there being any points on it?
Choosing points on a circle does not alter how the circle is defined; choosing a point does not create a gap in the circle.
The Man
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It in fact shows that the difference between the two self similar infinite convergent series is finite, that difference being the sum (particularly in the ½ common ratio series) of one of those self similar infinite series.
Again your simple assumption that “the infinite (that approaches the limit at its best)” is specifically what it proves false.
Actually he is correct , I did not see that post. However having seen it now I would have most likely just politely ignored it had I seen it then.
If you are insisting on some remarks Doron I can certainly oblige.
That was your assertion with your “reaching segment” requirement.
Again a partial sum of the infinite series like “1/2+1/4+1/8” still leaves a self similar infinite series as the remainder of the original infinite series. That self similar infinite series converges to a sum equal to the difference between the partial sum and the limit. Your “reaching segment” is just an infinite series of self similar segments, just as the entire original self similar infinite convergent series is.
The Man
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Nope just your inability to define a circle or any closed curve without points.
Again the difference between the two self similar infinite convergent series is finite, accurate and complete as the sum of one of those series.
Again complete refers specifically to the fact that nothing is missing that should be included. It is not a matter of “Quality” or “Quantity”, but simply inclusion or exclusion.
Again an infinite convergent series also has a sum that is both accurate and finite. Proven some 2,300 years ago.
Again simply an assumption (your “two values of the same size” requirement) you base on a finite number of values and again proven wrong some 2,300 years ago for an infinite convergent series.
doronshadmi
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Wrong.The Man said:
Complete refers to a non-composed thing (atomic) , where inclusion or exclusion refer to composed things, which are incomplete w.r.t to the non-composed.
Again your notion does not distinguish between the complete (the atomic) and the incomplete (the non-atomic) where this distinction is based on the qualitative difference between the atomic and the composed.
A point or a line are atomic exactly because no one of them is made by the other. The line is the simplest example of a non-local atomic quality and a point is the simplest example of a local atomic quality.
By your quantitative-only notion you count them and conclude that the thing that includes them is non-atomic.
You are right about that, because that thing is called a collection, and a collection is a non-atomic thing.
Since your abstraction ability can deal only with collections, you are unable to understand that the Non-local and Local atomic aspects are the minimal manifestations of the atomic state itself, which is beyond any manifestation (it is not Non-local AND not Local, or any other property that is used to define it).
Again, there is no such a thing like the entire collection of infinitely many things, exactly because the cardinality of infinitely many things (the 1+1+1+… form) has no sum, and it does not matter if things become smaller of bigger (in both cases biggest or smallest, do not hold).The Man said:
Simply wrong.The Man said:
If the sum between the limit and the partial sum equals to the partial sum you do not deal anymore with converge series, because you add two equal sizes to each other in order to reach the limit.
Converge series do no have any two equal sizes along it in order to be considered as a converge series. The sizes of converge series must be different from each other no matter how infinitely many scales are involved.
Archimedes did not understand the real nature self similarity over infinitely many scale levels. This self-similarity is defined only if being smaller is an invariant property upon infinitely many scale levels, which permanently prevent the value of a given limit.
This simple notion can easily be proven by researching, for example, Koch fractal.
Koch fractal is infinite only if there are infinitely many scale levels, where each scale level is represented by a given segment that is smaller than any arbitrary previous segment, for example:
The Koch fractal is an example of infinite extrapolation\interpolation of scale levels of the form …+1+1+1+… that has no sum.
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:
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doronshadmi
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EDIT:
Furthermore, Koch fractal can be found by using only non-locality (a single bended line):
Try to use only points (localities) in order to define Koch fractal, and you get no more than a single point (the line's bended levels are collapsed into a single point).
Koch fractal (finite or not) actually can be defined by using only a single line (non-locality), which is actually a 1-dim element over finite of infinitely many bended (scale) levels, which is not composed by segments AND no 0-dim is found along it (we do not need a point nor a segment in order to bend a line).
n= 1 to ∞
k = 0 to n-1
In general, we do not need k-dim elements or a collection of n-dim elements in order to define a bended n-dim element.
In that case the Koch fractal is some representation of the non-local atomic aspect, which is not the same as a Koch fractal that is defined by collections of n-dim elements or n-dim AND k-dim elements.
Furthermore, Koch fractal can be found by using only non-locality (a single bended line):
Try to use only points (localities) in order to define Koch fractal, and you get no more than a single point (the line's bended levels are collapsed into a single point).
Koch fractal (finite or not) actually can be defined by using only a single line (non-locality), which is actually a 1-dim element over finite of infinitely many bended (scale) levels, which is not composed by segments AND no 0-dim is found along it (we do not need a point nor a segment in order to bend a line).
n= 1 to ∞
k = 0 to n-1
In general, we do not need k-dim elements or a collection of n-dim elements in order to define a bended n-dim element.
In that case the Koch fractal is some representation of the non-local atomic aspect, which is not the same as a Koch fractal that is defined by collections of n-dim elements or n-dim AND k-dim elements.
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I don't know what word you mean, but I think it's neither band nor bend, certainly not banded or bended.
You also do need to define where to apply the rules to generate the fractal pattern, which means you do define the point at which to do so.
doronshadmi
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You are right, thank you, it has to be "bend".
Please refresh your screen and read it again.
doronshadmi
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At least it is consistently wrong now.
It is "consistently wrong" for any one who closed under the concopt of Collection.
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Can I quote you on that?
doronshadmi
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sympathic, 
doronshadmi
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You do not need me, this is exactly your reasoning.
The Man
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Complete can refer to your “atomic”, but it also refers “to composed things” that are, well, complete (nothing is missing).
Sure it does, it just doesn’t assume complete must be synonymous with your notion of “atomic”. Complete and incomplete are antonyms just as your “atomic” and “non-atomic” are. However both being antonyms does not make complete synonymous with your "atomic" or incomplete synonymous with your "non-atomic". Again the set {-15, 5} is complete as that set, but as the set of integers it is incomplete as most integers are missing from that set.
Again I’ve got no problems with your notion of a point being “atomic” (indivisible), but a line (or line segment) is divisible as line segments and that is the whole basis of the “Koch curve”.
Nope as expressed above.
Right about what? You ascribe some “quantitative-only notion” to me and call it “right”?
Wait, so your “atomic state itself” is “beyond any manifestation” “that is used to define it” meaning it need not be “atomic” or a “state” as those are just your ‘manifestations’ that you like to think you use to “define it”. So thanks Doron for admitting that your “atomic state itself” is not bound by your notion of “atomic” defining what you think ‘manifests’ an “atomic state”.
You are still confusing (again I think deliberately) the number of members in a set with a sum of those members.
Nope, you’re simply unable to understand what was written.
It is the difference between the limit and the partial sum that is itself a self similar infinite convergent series and in the case of the ½ common ratio series that remaining self similar convergent infinite series has a sum equal to the last element of the partial sum which is the difference between the partial sum and the limit (as already explained to you before).
Try actually reading the previous posts instead of just relating again your “two equal sizes” requirement that is just an assumption you have based on a finite number of elements.
Obviously he understood it better then you.
Again research is not just you imposing your assumptions of “no sum” on an infinite convergent series based on your (apparently deliberate) confusion between the number of elements in an infinite set (which is divergent) and the sum of those elements (that can be convergent) and your “two equal sizes” requirement based on the sum of a finite number of elements.
http://en.wikipedia.org/wiki/Koch_fractal
Oh look “divide the line segment” which is defined by points into three segments, also defined by points. A “triangle that has the middle segment from step 1 as its base” both defined by points then “remove the line segment that is the base of the triangle from step 2” which is defined by the end points of that segment.
Keep going Doron and let us know when you find that line segment not defined by points that you can’t divide into “three segments of equal length”. If you do then you’re simply not talking about a “Koch curve”.
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doronshadmi
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Thank you for demonstrating again how you are unable to directly get that is beyond any definition (now you will say that "that is beyond any definition" is this thing, but it is not, exactly as saying or thinking "silence" is not the thing itself).The Man said:
I have noticed that you did not write "the set of ALL integers", which is a good start in order to get OM.The Man said:
There is no such thing like infinite and complete class.
You still do not understand the following notion about completeness and incompleteness, for example:
A pointless circle is totally complete because is has no beginning AND no end (it has an atomic quality).
A circle with a single point along it defines a segment, and a closed segment is less complete than a pointless circle (completeness is a matter of Quality and not a matter of Quantity).
When more and more segments are used in order to define a circle, it becomes less and less complete, but as long as the amount of segments is finite, their added values have an accurate result known as Sum.
If an infinite amount of segments is used in order to define a circle, then also the accuracy of the result is lost and we do not have a Sum.
Since you notion is still closed under collections and classes, you are unable to get things from qualitative view and unable to understand the generalization of …+1+1+1+… form that stands at the basis of any infinite collection of distinct things (where this form is not limited to any particular class and therefore "missing" has no meaning at that abstraction level), which is beyond your partial and closed under collections and classes level).
Your abstraction is simply still closed under collections and classes.The Man said:
Simply wrong.The Man said:
Two equal sizes are exactly two equal sizes, whether a size is finite or not.
If you deal with two equal sizes, say bye bye to the concept of Convergence.
The Man said:
Again The Man, keep going and let us know when you are able to get thing beyond the reasoning that is closed under collections and classes.
Some hint: You will not find it in Wikipedia, which is a tool that includes only already agreed knowledge about some given subject.
Again, I have noticed that you wrote "the set of integers" instead of "the set of ALL integers" which is a good start in order to get OM.
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doronshadmi
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The whole basis of the “Koch curve” is exactly 1-dim that is bended over finite or infinitely many distinct scale levels, which are based on 1+1+1 (finite) or 1+1+1… (infinite) forms.The Man said:
Since you are unable to get the qualitative difference between the atomic and the collection, let us do it in 3D.
You have a closed 3D string, with no 3D bead along it.
In that case we say that the beadless closed 3D string is the atomic base ground for any collection of 3D beads along it.
Any amount of 3D beads along the closed 3D string does not divide it into many 3D strings.
All they do is to measure it by giving a bead an agreed value, and then we add these values to each other and define some size to that closed string.
Change the size of the beads, and you get different results, which are related to the same closed string.
But in any given measurement, the measured string is not divided by the beads along it, and stays a one and only one 3D closed atomic string under any given measurement.
The same notion holds aslo if 2D or 1D are used.
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doronshadmi
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The Man said:
No The Man, you simply do not get the general form that stands in the basis of (x/y)*(y/x).
For example if the considered case is (1/2^x), the general form is the result of the addition of the values, where each value is the result of (1/2^x)*(2^x/1), where (1/2^x) is the converges aspect and (2^x/1) is the diverges aspect of 1+1+1+... general form.
Again, your asymmetric view of this subject prevents from you to get the general form that stands at both converges or diverges series.
Maybe you can learn something form the great mathematician Poincaré (http://en.wikipedia.org/wiki/Henri_Poincaré), which understood geometric series better than Archimedes:
http://philmat.oxfordjournals.org/cgi/content/abstract/2/3/202
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Still waiting.
doronshadmi
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Try again, that doesn't answer the question I'm asking.
What has been achieved with OM? (Not, what do you think it might do.)
dafydd
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The only achievement so far is that it's given us all some good laughs.
All of Doron's answers to this question so far have led me to conclude that the achievements or practical applications of OM (except for the conventional strictly quantitative aspects of number) are non-local in nature, qualitative and inspirational.
Though, I seem to remember Doron saying that a positive contribution was liberation from the evils of mathematics as it has developed since Euclid strayed from the path.
Another answer he has given is that you, yourself are an example of ./__ Interaction. An amazing achievement!
(Bottom line: what we're asking of him is some "local only," "deductive," profane expectation that doesn't pertain to OM.
Or the question we are asking is incoprehensible to him.)
The Man
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No I will simply say "that is beyond any definition" is just a cop out for you so you can pretend for things to mean anything you want them to.
A mere oversight on my part as “the set of ALL integers” is clearly what I had intended.
Doron simply repeating your nonsense does not make it any less nonsense. If you find this nonsense makes you feel important, such that you can save our civilization from self-destruction. Then fine I’m happy for you, but don’t try to pawn it off as some new math, ethics or a combination of logic and ethics. It is just your fantasy.
Again “1+1+1+…” is a divergent series not a convergent series and a “qualitative view” does not mean you simply get to deliberately confuse a divergent series with a convergent one (ok well maybe in your fantasies it does) .
Again abstraction does not mean you just making up whatever you want and deliberately confusing the number of elements with the sum of those elements (again except of course just in your fantasies it does).
So you won’t try acctualy reading the previous posts.
Well since the sum of a convergent series is equal to a finite value, the only thing you would be saying “bye bye to” is your fantasies.
Sure as soon as you find a line segment that can’t be divided on a “Koch curve” instead of just fantasizing about one.
You should try actually reading that too sometime, you will find much disagreement about a lot of issues. Just whom do you think makes all these ‘agreements’ about knowledge anyway? Since generally no one accepts or agrees with your fantasies I can understand how you need to construe the general conformity of actual knowledge with some nefarious agreement.
Oh so now just not writing “ALL” “is a good start in order to get OM”? I wonder what else you don’t want anyone to write in order to enforce your “get OM” doctrine?
Nope, try actually reading.
Again simply repeating you string/bead analogy nonsense does not make it any less nonsense nor does adding the phrase “3D” to it. Who cares what you think your “string is not divided by”, line segments are still defined by points just as curves are (closed or not). Again it just shows how desperate you are to support you morbid fantasy of saving our civilization from self destruction. That you have to deliberately separate a line or curve from what define them, the points, just so you can combine them again into your “complex”.
Again “1+1+1+... “ is not convergent which means it is not a “general form” of convergence. Once again “general from” does not mean you simply get to deliberately confuse a convergent series with a divergent series (again except of course just in your fantasies). Again your asymmetric fantasy view makes you think a divergent series is a “general form” of a convergent series.
I’m sure I can (and have already as have many others), I’m sure you could as well, but I doubt you actually will. What does one reference to Cantor have to do with a geometric series?
And you think this is a argument for what? You just making up whatever crap you want and often attributing it as someone else’s “understanding” as well as you deliverable confusing the number of members of a set with the sum of the members of that set in addition to your simply ignorance that a divergent series is simply not convergent (‘generally’ or otherwise).
doronshadmi
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The "sum" of an infinite collection.The Man said:
In a diverges series each size is bigger than any arbitrary previous size.
In a converges series each size is smaller than any arbitrary previous size.
1+1+1+… is the general form of both cases, and it has no sum, if we deal with infinitely many sizes (diverges or converges, it does not matter).
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jsfisher
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Infinite sets don't exist in your universe, doron, remember? There can be no set of the integers (which necessarily would be all of them), there can be no set of the reals, there can be no infinite sets of any kind.
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