Deeper than primes

[The Man]

This constant (which is > 0) is exactly the reason that prevents from some geometric series to reach the value of a given limit.

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.

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).

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.

Once again you simply do not comprehend that defined by points does not infer it is made of points.

 

[sympathic]

I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.

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.

 

[doronshadmi]

Once again you simply do not comprehend that defined by points does not infer it is made of points.

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:

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 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.

 

[doronshadmi]

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.

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.

 

[jsfisher]

It has jsfisher, it has, care to re-comprehend it?

That does not parse.

 

[doronshadmi]

That does not parse.

That has nothing

It has (something)

Simple, isn't it?

 

[jsfisher]

Simple, isn't it?

Well, for those fluent in gibberish, I suppose it is. For everyone other than you, no.

 

[The Man]

Defined by points means that there is an infinite amount of segments that can't reach the value of the limit.

Nope, again simply your assumption and demonstrated to be wrong some 2,300 years ago.

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.

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?

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).

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.

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.

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:

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.

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?

 

[Apathia]

Nothing is obvious at the moment that you are opened to the infinite complexity that is based on Non-locality\Locality linkage.

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.

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).

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.

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]

There's no structure. There's just a place to stand for a better perspective.

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.

 

[The Man]

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.

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.

 

[doronshadmi]

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?

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.

 

[doronshadmi]

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.

Again your inability to get the atomic aspect, is rised?

 

[doronshadmi]

Remember the segments themselves approach the limit of zero length in the infinite convergent series.

Approach the limit, yes.

Reach the limit, no.

 

[Apathia]

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.

OK. Well at least I finally got that correct.

It has a structure-less foundation for better perspective of structures

.
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.

 

[jsfisher]

I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.

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?

 

[The Man]

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.

Again your simple assumption of such was proven wrong for a convergent infinite series some 2,300 years ago. Again the question was…

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?

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

Again your inability to get the atomic aspect, is rised?

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”).

Approach the limit, yes.

Reach the limit, no.

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”

 

[sympathic]

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.

At least I am in good company (Cantor)....

 

[doronshadmi]

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?

http://www.internationalskeptics.com/forums/showpost.php?p=5662065&postcount=8844

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=5662065&postcount=8844

No, that post points out how you mishandle standard mathematics to get the wrong answer. That isn't what I asked you. We already know you calculate very little correctly.

I asked you why you do it wrong then blame us,