Deeper than primes

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doronshadmi said:
This constant (which is > 0) is exactly the reason that prevents from some geometric series to reach the value of a given limit.
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That ratio, referred to as the common ratio of the series (which does not have to be >0), is exactly why we can conclusively demonstrate the result of that original series multiplied or divided by that common ratio is self similar with that original series. Meaning it is exactly why we can conclusively demonstrate that the convergent infinite series has a finite sum. Try reading the whole article and actually doing some more research on your own. Once again your simple assumptions do not constitute facts or proof.



From the article

The behavior of the terms depends on the common ratio r:

If r is between minus 1 and plus one the terms of the series become smaller and smaller, approaching zero in the limit. The series converges to a sum, as in the case above, where r is a half, and the series has the sum one.

If r is greater than one or less than minus one the terms of the series become larger and larger. The sum of the terms also gets larger and larger, and the series has no sum. (The series diverges.)

If r is equal to one, all of the terms of the series are the same. The series diverges.

If r is minus one the terms take two values alternately (e.g. 2, -2, 2, -2, 2,... ). The sum of the terms oscillates between two values (e.g. 2, 0, 2, 0, 2,... ). This is a different type of divergence and again the series has no sum.
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You will note that r = 1 is the common ratio for your divergent series 1+1+1+1… so it is certainly not the ‘same form’ as the convergent series 1/2+1/4+1/8+1/16… as you like to claim. You just can’t seem to get anything right about infinite geometric series (or you just don’t care to).


doronshadmi said:
And likw jsfisher, you also do not comprehend the size of each element that is based on 2^∞ cardinality (the cardinality of the continuum by your own paradigm) along a given infinite series of distinct values.
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Once again you simply do not comprehend that defined by points does not infer it is made of points.
 
The Man said:
Once again you simply do not comprehend that defined by points does not infer it is made of points.
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Defined by points means that there is an infinite amount of segments that can't reach the value of the limit.

But if the limit is reached by some segment, it means that one point that defines the segment is the limit point but the other point that defines the segment is not the limit point.

So we have two accurate values of the last segment, and we get the smallest segment (the absolute value of the limit point – the other point that defines the last segment).

In other words, The Man you still do not understand the results of your ill reasoning, because if the smallest segment is defined, then there is only a finite amount of segments.

EDIT:

The Man said:
your divergent series 1+1+1+1… so it is certainly not the ‘same form’ as the convergent series 1/2+1/4+1/8+1/16… as you like to claim.
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You just do not get that any infinite collection of distinct elements is based of 1+1+1+… form where each "1" symbolizes a distinct element, no matter what name, size, value, etc … it has.
 
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sympathic said:
It has been explained to you that in "standard math" ∞*0 is undefined (http://www.suitcaseofdreams.net/Infinity_Paradox.htm). The fact that you continue to ignore this just makes you come across as a fool.
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It has been explained to you that in "standard math" 1/∞ = 0 and as a result (∞*(1/∞)=∞*0) = (1=0).

The fact that you change the terms in the middle of the game (1/∞ = 0 is defined but ∞*0 or (∞*(1/∞) are undefined) just makes you come across as a fool.
 
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doronshadmi said:
Defined by points means that there is an infinite amount of segments that can't reach the value of the limit.
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Nope, again simply your assumption and demonstrated to be wrong some 2,300 years ago.


doronshadmi said:
But if the limit is reached by some segment, it means that one point that defines the segment is the limit point but the other point that defines the segment is not the limit point.
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Both points are always the limits of the segment they define. Remember the segments themselves approach the limit of zero length in the infinite convergent series.

Certainly in a finite series of segments one or two segments of the series will have a series limit or the series limits as a limit or the limits of that or those segments.

Is that your problem simply confusing a finite series of segments with an infinite series of segments approaching zero length?

doronshadmi said:
So we have to accurate values the last segment, and we get the smallest segment (the absolute value of the limit point – the other point that defines the last segment).
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Again we do not need a “last segment” to show that the infinite convergent series has a sum. Your simple assumption that it requires some “last segment” to do so is again simply your assumption and was proven wrong some 2,300 years ago.

doronshadmi said:
In other words, The Man you still do not understand the results of your ill reasoning, because if the smallest segment is defined, then there is only a finite amount of segments.
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Again Doron you still do not understand that the “ill reasoning”, the “smallest segment” (which you have not defined other then your “An expression like "0.000...1[base 2]”), your "last segment" (that has one of the series limits as one of its limits, which the 'first segment' would also have) and the requirement for a “a finite amount of segments” to reach a finite sum are all just your assumptions. The latter of which having been specifically proven as false some 2,300 years ago.


ETA:

doronshadmi said:
EDIT:


You just do not get that any infinite collection of distinct elements is based of 1+1+1+… form where each "1" symbolizes a distinct element, no matter what name, size, value, etc … it has.
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You just don’t understand or again just don’t care that we are discussing the sum of a convergent infinite series which is specifically not divergent and thus specifically not “based of 1+1+1+… form” regardless of what you think “each "1" symbolizes”.


Also ETA:

Is that your problem Doron, not being able to distinguish (perhaps deliberately) between the number of elements being divergent while the sum of those elements is convergent?
 
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doronshadmi said:
Nothing is obvious at the moment that you are opened to the infinite complexity that is based on Non-locality\Locality linkage.
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I must conclude that my request:
I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity.
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Shows a substantial misunderstanding of Organic Mathematics.
I and the others here keep asking you to show OM in action, show us how its approach to0 problem solving works.

Your answer is nearly always of the form of Something/Something Else Interaction is the foundation.
We are never satisfied because we're expecting a structure on that foundation.
If someone says they're doing Mathematics, we can't help but expect structure, results, and applications.
But OM is no methodology.
It's as you said a tool to encourage awareness.
There's no structure. There's just a place to stand for a better perspective.

So all that's asked is that I dismiss analytic thought by classes and categories and see the Complex, non-linear view of x/!x Interaction.

This is fully in line with OM's continual use of mathematical terms in metaphorical and figurative ways. And the equivocation I spoke of where "memory" and "non-local" are practically interchangeable.

The application of OM:
See numbers this way and you will be more self-aware.
Dismiss category thinking for x/!x Interaction thinking and you will dismiss biases and discrimination.
Free yourself from analytic only thinking by embracing the x/!x Interaction, and you will have endless potential.

Get the "Direct Perception" and you will be able to see where things are in the Complex and go there right away.

I suppose the only method as such would be that you could sit down and make a chart based on whatever interacting principles were relevant.
This isn't mathematics, though.
It's primarily a philosophy using some mathematical language in unique and figurative ways.

By OM you develop your ability to cherish the inflation's-free value non-trivial result of the interaction between the simple and the complex, known as personality, where this personality has a unique knowledge of the researched, which helps each personality (the same and also other personality) to be developed beyond any limited dogma of a given realm (abstract or not).
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Alas, this so much reminds me of when I was an aspyesque teen trying to cram my conflicting emotions and relationships into some kind of intellectual framework.


You still miss it.

A quantity is the result of the linkage of different qualities known by OM as Non-locality and Locality.

The quantitative result can be accurate or not, but is does not change the fact about the qualitative foundation of Quantity.
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Didn't miss it. Said it myself, so you wouldn't have to.

But I'm not going to ask for a demonstration of using a number in its qualitative aspect again. They are just quantities or potential quantities.
 
doronshadmi said:
It a structure-less foundation for better perspective of structures, which is something that you still can't get.

At the moment that you get it, you are able to understand http://www.internationalskeptics.com/forums/showpost.php?p=5660394&postcount=8824.
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Got that a long time ago Doron, which is why I keep reminding you that you have no basis for your assertions just within your own notions, by your own assertions. Again “a structure-less foundation” is not a foundation as it simply does not support anything (it has no support structure) including just your own assertions and notions.
 
The Man said:
Is that your problem Doron, not being able to distinguish (perhaps deliberately) between the number of elements being divergent while the sum of those elements is convergent?
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Your problem is that you simply do not understand that an infinite number of added elements (where each one of them > 0) has no sum.
 
The Man said:
Got that a long time ago Doron, which is why I keep reminding you that you have no basis for your assertions just within your own notions, by your own assertions. Again “a structure-less foundation” is not a foundation as it simply does not support anything (it has no support structure) including just your own assertions and notions.
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Again your inability to get the atomic aspect, is rised?
 
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The Man said:
Remember the segments themselves approach the limit of zero length in the infinite convergent series.
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Approach the limit, yes.

Reach the limit, no.
 
doronshadmi said:
It has a structure-less foundation for better perspective of structures, which is something that you still can't get.

At the moment that you get it, you are able to understand http://www.internationalskeptics.com/forums/showpost.php?p=5660394&postcount=8824.
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OK. Well at least I finally got that correct.
It has a structure-less foundation for better perspective of structures
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.
Specifically what you call the Complex, which is not a structure in the analytic way.

I was trying to see if it could be built upon, but building upon it is definitely contraindicated.
It's not that kind of foundation. It's a fundamental.
 
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doronshadmi said:
I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.
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Ok, since general challenges to this ridiculous remark lead to gibberish responses, let's see if we can approach it in baby steps. Something suitable for a 5-year-old.

Doron,
You said that by our "ill reasoning" there are two different reductions, as follows:
∞*(1/∞) -> ∞ * 0 -> 0, and
∞*(1/∞) -> (∞*1)/∞ -> ∞ / ∞ -> 1​
Is that right, or did you have a different set of reductions in mind?

Now, please note that these reductions are not consistent with what you continually deride as standard mathematics. By either reduction, we get an undefined result. Consistency is maintained.

So, why are you blaming the rest of us for your inability to get it right?
 
doronshadmi said:
Your problem is that you simply do not understand that an infinite number of added elements (where each one of them > 0) has no sum.
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Again your simple assumption of such was proven wrong for a convergent infinite series some 2,300 years ago. Again the question was…


The Man said:
Is that your problem Doron, not being able to distinguish (perhaps deliberately) between the number of elements being divergent while the sum of those elements is convergent?
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You could actually try answering it this time. However, from your response my surmise would be that you are unable to distinguish (perhaps deliberately) between the number of elements being divergent while the sum of those elements is convergent



doronshadmi said:
Again your inability to get the atomic aspect, is rised?
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Again your inability to keep your “atomic aspect” (by dividing it into two aspects), well, “atomic” (indivisible by your own assertions) has been raised on several occasions (as well as the obvious failure of your “trunk/branch” analogy”).

doronshadmi said:
Approach the limit, yes.

Reach the limit, no.
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Again if the fractional value being added is zero then the sum limit of 1 must have already been reached with a pervious fractional value. You have been the only one claiming the fractional value of zero must be reached for the series to have a sum. So is your problem simply your inability to distinguish (again perhaps deliberately) between the different limits, the number of elements being divergent to infinity, the sum being convergent to the finite value of 1 and the fractional values decreasing to the limit of zero? You assumption and confusion seem to be (again perhaps deliberately) that since the divergent series of the number of elements has no sum (in the ordinary sense) and that the fractional value being added can not reach zero before the sum limit has been reached, that the sum limit can not be reached and the infinite convergent series has no sum. Again an assumption proven to be wrong some 2,300 years ago.

In fact, as usual, your own assertions simply contradict your own assertions. You claim the convergent infinite series “has no sum” yet proclaim that “the infinite series of added sizes is permanently smaller than the value of the given limit”.

So which is it Doron that it has “no sum” and thus you can make no references to it being “permanently smaller than the value of the given limit” or it has a sum that is “smaller than the value of the given limit”? As usual you simply want it both ways, to assert that it has “no sum” yet draw a conclusion “smaller than the value of the given limit” based on your simple assumption of a sum “smaller than the value of the given limit”
 
doronshadmi said:
It has been explained to you that in "standard math" 1/∞ = 0 and as a result (∞*(1/∞)=∞*0) = (1=0).

The fact that you change the terms in the middle of the game (1/∞ = 0 is defined but ∞*0 or (∞*(1/∞) are undefined) just makes you come across as a fool.
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At least I am in good company (Cantor)....
 
jsfisher said:
Ok, since general challenges to this ridiculous remark lead to gibberish responses, let's see if we can approach it in baby steps. Something suitable for a 5-year-old.

Doron,
You said that by our "ill reasoning" there are two different reductions, as follows:
∞*(1/∞) -> ∞ * 0 -> 0, and
∞*(1/∞) -> (∞*1)/∞ -> ∞ / ∞ -> 1​
Is that right, or did you have a different set of reductions in mind?

Now, please note that these reductions are not consistent with what you continually deride as standard mathematics. By either reduction, we get an undefined result. Consistency is maintained.

So, why are you blaming the rest of us for your inability to get it right?
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http://www.internationalskeptics.com/forums/showpost.php?p=5662065&postcount=8844
 
The Man said:
As usual you simply want it both ways, to assert that it has “no sum” yet draw a conclusion “smaller than the value of the given limit” based on your simple assumption of a sum “smaller than the value of the given limit”
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Sum is a result of a finite addition that reaches the value of a given limit, by finitely many steps.

Proportion is a result of an infinite addition that approaches the value of a given limit, by infinitely many steps.

“smaller than the value of the given limit” is not a sum, but it is a proportion, which is possible exactly because the added values > 0 have no sum (they do not reach the limit, exactly because we deal with infinitely many elements).

As for the Archimedean "proof":

The Man said:
What I (or more specifically Archimedes) did was multiply the series 1/2+1/4+1/8+1/16… by 2 meaning just adding it to itself.
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What you are doing is this:

4394565223_68d292444a_o.jpg


So as you see, nothing is changed, in both cases the added values only approach the limit (whether it is 1 or 2).
 
jsfisher said:
Yes, your post does clearly show you get it wrong. No question about that. None at all. Again, my question was why do you blame us for your inability to follow simple rules?
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Rules? you change the rules in the middle of the game so blame only yourself.
 
doronshadmi said:
Rules? you change the rules in the middle of the game so blame only yourself.
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You clearly don't like the rules, but they don't change, and certainly not in the middle of the game. As I stated before, it is solely a case of you being unable to follow them. Please don't blame us for your failings.
 
doronshadmi said:
Sum is a result of a finite addition that reaches the value of a given limit, by finitely many steps.
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Again your simple assumption was proven wrong for a convergent infinite series some 2,300 years ago.

doronshadmi said:
Proportion is a result of an infinite addition that approaches the value of a given limit, by infinitely many steps.
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No proportion is the result of being, well, proportional. Apparently you simply do not understand that reaching some limit from some other value (with other values in between) specifically requires approaching that limit. Again approaching and reaching are not mutually exclusive.

doronshadmi said:
“smaller than the value of the given limit” is not a sum,
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It is a statement about the sum that it is “smaller than the value of the given limit”


doronshadmi said:
but it is a proportion,
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That would be another statement about the sum, which in the convergent series being discussed is a fractional value. You do understand that 1 to 1 (1/1) is a proportion, don’t you?

doronshadmi said:
which is possible exactly because the added values > 0 have no sum (they do not reach the limit, exactly because we deal with infinitely many elements).
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Again your simple assumption was proven wrong for a convergent infinite series some 2,300 years ago.


doronshadmi said:
As for the Archimedean "proof":




What you are doing is this:

[qimg]http://farm3.static.flickr.com/2436/4394565223_68d292444a_o.jpg[/qimg]
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No Doron that is just what you are doing, and once again by using a circle (or closed curve) you are asserting the circumference to be complete (that’s what makes it a circle or closed curve).


doronshadmi said:
So as you see, nothing is changed, in both cases the added values only approach the limit (whether it is 1 or 2).
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I see your one circle has a circumference of one and the other a circumference of two, meaning the circumference has increased by 1.

Again the proof is based on the fundimetal relations of1/2+1/4+1/8+1/16… =1/2+1/4+1/8+1/16… (one of your favorites) and 1/2+1/4+1/8+1/16… + 1/2+1/4+1/8+1/16… – (1/2+1/4+1/8+1/16… ) = 1/2+1/4+1/8+1/16… . In order to refute the proof you are going to have to show one of those relations to be false. So Doron which one is it? Drawing circles that you simply assume to be incomplete with an infinite number of elements is no different than your simple (and proven false) assumption that an infinite convergent series has no sum. Again your simple assumptions do not constitute proof and they certainly do not constitute the refutation of a proof.
 
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The Man said:
Apparently you simply do not understand that reaching some limit from some other value (with other values in between) specifically requires approaching that limit.
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Not if approaching is a permanent state, and this is exactly the permanent state of proportion, in the case of the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…) as clearly shown in:
4394565223_68d292444a_o.jpg


In order to reach the limit in one of those geometric series, the reaching segment has to be at least in the same size of the previous segment, as clearly shown the diagrams above. But then we have a finite amount of segments.

Since any arbitrary segment along the infinite geometric series above is smaller then any arbitrary previous segment, and "being smaller then any arbitrary previous segment" is a permanent state of the infinite geometric series above, then those series do not reaching the value of the limit.

In other words, Archimedes did not prove anything about the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…).
 
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jsfisher said:
Yes, your post does clearly show you get it wrong. No question about that. None at all. Again, my question was why do you blame us for your inability to follow simple rules?
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jsfisher, 1/∞ = 0 is defined but ∞*0 or ∞*(1/∞) are undefined, and this is done by your community.

Can you explain such inconsistency?
 
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doronshadmi said:
jsfisher, 1/∞ = 0 is defined but ∞*0 or ∞*(1/∞) are undefined, and this is done by your community.
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More correctly, 1/∞ is defined to be 0, while neither 0*∞ nor ∞/∞ are defined. Why does this trouble you? Do you also have difficulty dealing with 3/0 as being undefined?

Can you explain such inconsistency?
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You haven't yet pointed out any inconsistency.


Also, what does any of this have to do with your bogus claim?
 
jsfisher said:
Also, what does any of this have to do with your bogus claim?
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What any of your false game (1/∞ is defined to be 0 (written as 1/∞=0), but ∞*(1/∞) or ∞*0 of ∞*(1/∞)=∞*0 are undefined) has to do with real reasoning?
 
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doronshadmi said:
What any of your false game (1/∞ is defined to be 0 (written as 1/∞=0), but ∞*(1/∞) or ∞*0 of ∞*(1/∞)=∞*0 are undefined) has to do with real reasoning?
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You continue to evade the question. You make a bogus claim, and you can't back it up. Again you prove yourself an incompetent liar, and, since you cannot see the reasoning behind an elementary extension to basic arithmetic, an incompetent mathematician.
 
doronshadmi said:
Not if approaching is a permanent state, and this is exactly the permanent state of proportion, in the case of the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…) as clearly shown in:
[qimg]http://farm3.static.flickr.com/2436/4394565223_68d292444a_o.jpg[/qimg]
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It is not “a permanent state”, once again your simple assumption that it is “a permanent state” (meaning the series has “no sum”), was proven wrong for a convergent geometric series some 2,300 years ago.

doronshadmi said:
In order to reach the limit in one of those geometric series, the reaching segment has to be at least in the same size of the previous segment, as clearly shown the diagrams above. But then we have a finite amount of segments.
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Nope it just has to be the same size as the remaining gap when “we have a finite amount of segments”, but we are not talking about a finite number of segments. Again Doron you are still focusing on your own concept of a ‘last segment’ which again has no relevance in an infinite series (there is no definable ‘last segment’).

Again do some research on your own. Let’s take the series 1/8+1/16+1/32… which is just what remains of your original series after the partial sum of ½+1/4 is removed. In other words the series 1/8+1/16+1/32… is one quarter of the original series and exactly equal to the “last segment” of that ½+1/4 partial sum as well as the reamining gap to the limit. Do it for any partial sum of your original series and you will find it is always the case. The remaining amount of that partial sum from the limit is exactly equal to the resulting infinite series after that ‘last segment’ of that partial sum and the sum of that new infinite series also equals that ‘last segment’ of the partial sum. So what ever ‘last segment’ you chose of the infinite series (resulting in a partial sum) the remaining infinite series is equal to the remaining gap as well as that ‘last segment’. Simply put your subsequent argument fails for an infinite series just as a definition for a ‘last segment’ does.





doronshadmi said:
Since any arbitrary segment along the series is smaller then any arbitrary previous segment, and "being smaller then any arbitrary previous segment" is a permanent state of an infinite series, then those series do not reaching the value of the limit.
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Since your concept of a ‘last segment’ is inapplicable to the infinite series so too is the above restriction you assert from the misapplication of that concept to the infinite series. Is that your problem Doron just you misapplying a concept from a finite series (or partial sum) to an infinite series?



Doron the reason you make the assumption you do (that an infnite convergent series has “no sum”) is irrelevant to the fact that it has been proven wrong some 2,300 years ago. One could also make the assertion that with each additional segment the series has a sum (referred to as a partial sum) thus the infinite series should also have sum. Now you may claim, and you do, that such an infinite sum is less than the limit of that series. However those too are simply assumptions based on certain aspects of the series, that the infinite series has a sum and that it is less than the limit. If only there was a way to use the relationships of that series to prove if the infinite series has a sum or not and if it is equal to the limit or not. Oh wait, there is and it was found some 2,300 years ago.

doronshadmi said:
In other words Archimedes did not prove anything about the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…).
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He proved your assumption that a convergent infinite series has no sum is just wrong and that we can find that sum based on the common ratio. Since your assertion that the two times series (1/1+1/2+1/4+1/8+1/16…) has “no sum” is based solely on your assumption that the series 1/2+1/4+1/8+1/16… has “no sum” and that assumption was proven wrong some 2,300 years ago, it just makes your assertion that the two times series (1/1+1/2+1/4+1/8+1/16…) has “no sum” twice as wrong. Your assertions still amount to you simply claiming your assumption is correct only because you assume it to be correct.
 
doronshadmi said:
Since any arbitrary segment along the series is smaller then any arbitrary previous segment, and "being smaller then any arbitrary previous segment" is a permanent state of an infinite series, then those series do not reaching the value of the limit.
The Man said:
Since your concept of a ‘last segment’ is inapplicable to the infinite series
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Excuse me ??

Where exactly do you find a 'last segment' in the quote above, taken from my post?


The Man said:
Again Doron you are still focusing on your own concept of a ‘last segment’ which again has no relevance in an infinite series (there is no definable ‘last segment’).
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Exactly The Man. And this is the exact reason of why a finite amount of segments reaches the limit, and an infinite amount of segments does not reach the limit (there is no definable ‘last segment’ exactly because "smaller" is an invariant property of an infinite amount of added and converge elements > 0).

The Man said:
However those too are simply assumptions based on certain aspects of the series, that the infinite series has a sum and that it is less than the limit.
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The Man, you are the one who using an assumption taken form a finite series (which has a sum) and force it on an infinite series, that has no sum exactly because it inherently incomplete.

Archimedes did not prove anything about the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…), and the reason for this is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5667833&postcount=8867.

Your limited reasoning simply can't grasp infinite interpolation where "smaller" is its invariant state, no matter
how infinitely many converge elements > 0 are added.

The Man said:
the remaining infinite series is equal to the remaining gap as well as that ‘last segment’.
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You simply assert that the remaining infinite series has a sum (as if it was a finite series) and then you are using this wrong assumption to reach the value of the limit.
 
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jsfisher said:
You continue to evade the question. You make a bogus claim, and you can't back it up. Again you prove yourself an incompetent liar, and, since you cannot see the reasoning behind an elementary extension to basic arithmetic, an incompetent mathematician.
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It is a valid claim, your school of thouht plays a false game (1/∞ is defined to be 0 (written as 1/∞=0), but ∞*(1/∞) or ∞*0 of ∞*(1/∞)=∞*0 are undefined).
 
doronshadmi said:
Excuse me ??

Where exactly do you find a 'last segment' in the quote above, taken from my post?




Exactly The Man. And this is the exact reason of why a finite amount of segments reaches the limit, and an infinite amount of segments does not reach the limit (there is no definable ‘last segment’ exactly because "smaller" is an invariant property of an infinite amount of added and converge elements > 0).



The Man, you are the one who using an assumption taken form a finite series (which has a sum) and force it on an infinite series, that has no sum exactly because it is infinite and therefore inherently incomplete.

Archimedes did not prove anything about the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…), and the reason for this is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5667833&postcount=8867.

Your limited reasoning simply can't grasp infinite interpolation where "smaller" is its invariant state, no matter
how infinitely many converge elements > 0 are added.
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http://school.maths.uwa.edu.au/~berwin/humour/invalid.proofs.html

Some of Doron's favorites:

1.19 Proof by picture
A more convincing form of proof by example. Combines well with proof by omission.
1.20 Proof by vehement assertion
It is useful to have some kind of authority in relation to the audience.
 
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doronshadmi said:
Excuse me ??

Where exactly do you find a 'last segment' in the quote above, taken from my post?
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Excuse me ??

Where did I claim you used the phrase “'last segment” in that post?

Are you claiming that your “reaching segment” would not be the 'last segment' in that series for you?


doronshadmi said:
Exactly The Man. And this is the exact reason of why a finite amount of segments reaches the limit, and an infinite amount of segments does not reach the limit (there is no definable ‘last segment’ exactly because "smaller" is an invariant property of an infinite amount of added and converge elements > 0).
Click to expand...

Again demonstrating the invalidity of your 'last segment' or if you prefer “reaching segment” argument for an infinite series.


doronshadmi said:
The Man, you are using an assumption, taken form a finite series (which has a sum) and force it on an infinite series, that has no sum exactly because it is infinite and therefore inherently incomplete.
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Doron I told you those were assumptions just as your assumptions are. The difference is you’re the only using and depending upon any of those assumptions. No one need assume a convergent infinite series has a sum or not when it is quite easy to prove that indeed it does have a finite sum.


doronshadmi said:
Archimedes did not prove anything about the infinite geometric series 0+1/2+1/4+1/8+… (or 0+1/1+1/2+1/4+…), and the reason for this is clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=5667833&postcount=8867.
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Again he proved that the assumptions you base that post on are simply false.



doronshadmi said:
Your limited reasoning simply can't grasp infinite interpolation where "smaller" its invariant state, no matter how infinitely many converge elements > 0 are added.
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Doron your limited reasoning simply can’t grasp that you simply assuming something for whatever reason does not constitute proof and certainly does not refute the given proof. Again in order to refute the given proof you would have to show that one or both of the two basic mathematical relationships it is base on (X=X and X+X-X=X) are wrong. So again, which one is wrong for you?
 
sympathic said:
http://school.maths.uwa.edu.au/~berwin/humour/invalid.proofs.html

Some of Doron's favorites:

1.19 Proof by picture
A more convincing form of proof by example. Combines well with proof by omission.
1.20 Proof by vehement assertion
It is useful to have some kind of authority in relation to the audience.
Click to expand...

More nonsense from a community of people that enable to deal with abstraction only by using a very limited and specific way.

In other words, this community of people dependents on specific tools, which actually are nothing but a reflection of their own limitations to deal with abstraction, which is actually independent on any specific tool.
 
The Man said:
(X=X and X+X-X=X) are wrong. So again, which one is wrong for you?
Click to expand...

X+X is the right incomplete series and X is the left incomplete series in the following diagram:

[qimg]http://farm3.static.flickr.com/2436/4394565223_68d292444a_o.jpg[/qimg]


The Man said:
Excuse me ??

Where did I claim you used the phrase “'last segment” in that post?
Click to expand...

http://www.internationalskeptics.com/forums/showpost.php?p=5668104&postcount=8872 your 3th part of your reply.
 
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doronshadmi said:
More nonsense from a community of people that enable to deal with abstraction only by using a very limited and specific way.

In other words, this community of people dependents on specific tools, which actually are nothing but a reflection of their own limitations to deal with abstraction, which is actually independent on any specific tool.
Click to expand...

Look around you, and especially straight ahead at your computer, Doron, the world you live in was built using these tools that you dismiss because you don't understand them.

Now, exactly what has ever been accomplished with OM?
 
zooterkin said:
Look around you, and especially straight ahead at your computer, Doron, the world you live in was built using these tools that you dismiss because you don't understand them.

Now, exactly what has ever been accomplished with OM?
Click to expand...

It was built by using only finite tools (no infinite extrapolation\interpolation).

I am talking about the technology beyond the finite, which starts by dealing with infinite extrapolation\interpolation, which are inherently incomplete.
 
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