Deeper than primes

[dafydd]

What do you mean by "more to it than merely that"?

Now who can't comprehend written language?

 

[doronshadmi]

“permanently in a state of being smaller” would make it the “smallest” in your notions.

No, it would make it the “smallest” in your notions, The Man.

Furthermore, we can also understand "smaller than … in the usual sense, such that any arbitrary given size is > 0 AND smaller than any arbitrary previous size of an infinite series of distinct sizes.

In other words, the infinite series of added sizes is permanently smaller than the value of the given limit, no matter how many distinct sizes > 0 are involved.

Also please show us the proof of Archimedes about this subject.

 

[zooterkin]

Also please show us the proof of Archimedes about this subject.

You've already had it.

 

[doronshadmi]

Fortunately I was able to cobble that together out of your oblique reply.

I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity.

Is there a particular reason of why do you continue to ignore, for example, http://www.scribd.com/doc/17039028/OMDP , http://www.scribd.com/doc/21967511/...considerations-of-Some-Mathematical-Paradigms or

 

[doronshadmi]

You've already had it.

This

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.

is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).

 

[The Man]

No, it would make it the “smallest” in your notions, The Man.

Then you must have something smaller in your notions. What is it? Remember the questions was…

You contend that the convergent infinite sum never reaches the limit so it must have some “smallest segment” that is the difference between that infinite sum and the limit. So Doron what is your “smallest segment”?

Furthermore, we can also understand "smaller than … in the usual sense, such that any arbitrary given size is > 0 AND smaller than any arbitrary previous size of an infinite series of distinct sizes.

So just what would “"smaller than …” mean in your ‘unusual sense’?

In other words, the infinite series of added sizes is permanently smaller than the value of the given limit, no matter how many distinct sizes > 0 are involved.

Already conclusively demonstrated to be false for a convergent infinite series some 2,300 years ago.

Also please show us the proof of Archimedes about this subject.

Already done numerous times, do some actual research yourself. Here is the link again as you seem to be unable to find it yourself.

http://en.wikipedia.org/wiki/Geometric_series#Sum

 

[jsfisher]

This

is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).

Much like analogies, Doron doesn't cope well with proofs, either.

 

[The Man]

This

is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).

Doron, again if you are asserting a circumference you are asserting that limit (the circumference) is being reached. Otherwise it is simply not a circumference (distance around a closed curve).

Again Doron your focus is on the infinite activity of adding the fractional values, your old infinite list can not be completed dodge. One does not need to perform an infinite number of additions to show that an infinite convergent series has a finite sum, as already demonstrated.

In fact if the infinite series of additions can not be completed by you then the infinite series of multiplications can not be completed by you either. Thus your claim of “It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2” is false by your own assertions of your own limitations. Just as before, the continuing infinite activity you depend upon to keep you from reaching the limit 1 also prevents you from changing that limit to 2 by an infinite series of multiplications, which are actually just an infinite series of additions (each fractional value added to itself). You can’t have it both ways Doron, the requirement for an infinite series of additions prevents you from reaching the limit but the requirement for an infinite series of additions does not prevent you from changing the limit from 1 to 2.

Since the basic mathematical principles used in the self similarity proof are that 1/2+1/4+1/8+1/16… = 1/2+1/4+1/8+1/16... 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…. You are going have to prove one of those fundamental mathematical relationships to be wrong. Again this is very simple and basic math. That you seem to have such a demonstrative problem with it simply confirms that you just do not comprehend mathematics. You simply assuming “we did not reach the limit value 1” does not constitute proof that “we did not reach the limit value 1”. Just as you simply claiming “now we simply do not reach the limit value 2” based on your simple assumption that “we did not reach the limit value 1” does not constitute proof of anything other than you like to make assumptions and claim they are valid, without any proof.

 

[Apathia]

Is there a particular reason of why do you continue to ignore, for example, http://www.scribd.com/doc/17039028/OMDP , http://www.scribd.com/doc/21967511/...considerations-of-Some-Mathematical-Paradigms or

[qimg]http://farm5.static.flickr.com/4047/4390093906_6c3ae0ab88_o.jpg[/qimg]
[qimg]http://farm5.static.flickr.com/4006/4389327007_f968923c21_o.jpg[/qimg]

I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity. In your little paper cited above, it's clear that numbers are being used to quantitave ends.

At best what I'm getting from this is that a number can be used notationally or nominatively (instead of merely cardinaly and ordinaly). A number can be used as a marker of a bead idependent of the count of beads.

Perhaps more qualitatively, a number an be used adjectivally to code the degree of some quality.
For example a color code that identifies the degree of hue.
In this particular context, there is a meaning to the addition of hue 3 and hue 2. There is a resulting lightening or darkening of hue to another code value.
So numbers in certain contexts can be used to identify value.
This is a qualitative/relational/symbolic use of number.
Of course ordinary language does this frequently.

But I take it that's not much of what you want to make of it.

Sure, without a memory/object interaction in which I remember both the beads I've counted as opposed to the beads I haven't, and the count so far, I can't count or come to a definite sum. And yes we need to be aware of the individual item included in the count.
But this is too obvious and general a point to be an applied application.

A. How do I ballance my need for an income with right livelihood and my desire to have creative employment?
B. Simple! It's a memory/object interaction!

But I think your point is something more like this:
If I'm thinking in a non-linear fashion, I won't be bound to a step by step counting process but will see the wider view of non-linear associations.
If I stop to smell the roses, I'll find a complex of associations and associative pathways I've ignored and within that a novel solution.

We all do this in the process of solving problems more difficult than quantity calculation.
I'm not sure that stoping each time I do addition to note all the possible this one was coiunted-this one wasn't combos, is going to raise my awareness very much.

As I've said before, the key ethical essence isn't in how I count objects, but in how I regard persons.

But if your turning of simple arithmatic into a complex noting all ther possible configurations of of what was and what wasn't remembered as counted, helps you be aware that you are an active person and not a mere calculating machine, I cannot deny you the value of your ritual.

 

[Apathia]

You're also saying, it seems, that conventional math "leaps" to and deals only with situations where quantity and order are defined and clearly known.
But your ONs include the situations where there is an ambiguity or the sums aren't simply clear and are uncertain.

I would not call such a circumstance a matter of quality as opposed to quantity.
It's merely uncertain quantity of objects. (Because of uncertainty enetered into the count.)
And a quantity held in memory is a quantity not a quality.
(Yes, I know the number is quantity and quality because they are generated by the Quality/Quantity Interaction. But what is the actual use you are making of it?)

What it seems you are calling for is a way of seeing in which numbers aren't signify more value than just the price tag at Wal-mart. Number must exhibit an ethical dimension and have an ontological meaning.

Ordinarity, a combo of qualtative and quantitative uses of number would look something like this:
We'd talk about a quality 3 DVD collection of the 3 Lord of The Rings movies.

A problem that arrises again and again in all this is that non-locality and quality are not synonomus concepts and don't fit together like peas in a pod.
I do equivocation in trying to make something coherent out of what you are saying, but you are doing a great deal of equivocation yourself.
We both should stop and smell the roses and the complexity we siumplify away.

 

[doronshadmi]

Doron, again if you are asserting a circumference you are asserting that limit (the circumference) is being reached.

Only by a finite amount of steps.


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

In fact if the infinite series of additions can not be completed by you then the infinite series of multiplications can not be completed by you either. Thus your claim of “It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2” is false by your own assertions of your own limitations.

In fact you don't get that 1 or 2 are finite values, that are reached only by finite steps.

Already conclusively demonstrated to be false for a convergent infinite series some 2,300 years ago.

Not even in your dreams.

http://en.wikipedia.org/wiki/Geometric_series#Sum

The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant.

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

 

[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.

Why do you continue to trot out this same example and claim that it is by our "ill reasoning" that the inconsistency occurs? I don't get that result. It is only by disregarding actual Mathematics that you get the silly result. It is just your ill reasoning that continues to produce this invalid result.

 

[doronshadmi]

But this is too obvious and general a point to be an applied application.

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

As I've said before, the key ethical essence isn't in how I count objects, but in how I regard persons.

EDIT:

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).

And a quantity held in memory is a quantity not a quality.

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.

 

[zooterkin]

By OM you develop your ability to cherish the inflation's-free value the non-trivial result of the interaction between the simple and the complex, known personality, where this personality has a unique knowledge of the researched, which helps each personality to be developed beyond any limited dogma of a given realm (abstract or not).

Waiter! I ordered Waldorf, not Word.

 

[doronshadmi]

Why do you continue to trot out this same example and claim that it is by our "ill reasoning" that the inconsistency occurs? I don't get that result. It is only by disregarding actual Mathematics that you get the silly result. It is just your ill reasoning that continues to produce this invalid result.

jsfisher, I see that you 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.

 

[doronshadmi]

Waiter! I ordered Waldorf, not Word.

A fresh ftfyFTFY is on its way to your table.

 

[The Man]

Only by a finite amount of steps.

So then you are simply not talking about an infinite series and your assertions are irrelevant in that regard, by your own assertion above

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

I see you are still trying to posit your own deliberately “invalid result” of your own “ill reasoning” onto others.

In fact you don't get that 1 or 2 are finite values, that are reached only by finite steps.

Again conclusively demonstrated as false some 2,300 years ago, again your simple assumptions do not constitute facts or proof.

 

[doronshadmi]

http://en.wikipedia.org/wiki/Geometric_series#Sum

The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant.

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

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.

 

[jsfisher]

jsfisher, I see that you 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.

That has nothing to do with my question to you. Care to try again?

 

[doronshadmi]

That has nothing to do with my question to you. Care to try again?

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