Deeper than primes

[jsfisher]

No problem.

If approaches is a constant property, then w ≠ 0 and F(w) has no limit.

So how do limits work in your world?

By your "reasoning" X ≠ AND = 0.

Not even close.

 

[jsfisher]

Again your step-by-step reasoning? (maybe a better name is stop-by-stop).

The steps were provided by you, not me. The fact they didn't agree with your drawing is your problem, and yours alone. Don't blame any of us for your failures.

 

[jsfisher]

Wow.

Jsfisher is the voice of the choir in some Sophocles' tragedy.

Prove my statement wrong. Do show us how limits work in doronetics.

 

[doronshadmi]

Prove my statement wrong. Do show us how limits work in doronetics.

Here is the right way to get the value (and the concept) of Limit.

Two sizes of the same incompleteness have result 0 if they are subtracted from each other.

The real problem here is 1 – (1/2+1/4+1/8+…) and Archimedes did prove that it = 0.

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:

In other words:

1 – (1/2+1/4+1/8+1/16+…) > 0

2 - (1/1+1/2+1/4+1/8+...) > 0

4 - (2/1+1/1+1/2+1/4+...) > 0

...

etc. ad infinituum.


If one reaches the value of the limit, then one does not use an infinite convergent series, because in order to reach the limit's value one uses for example:

1 – (1/2+1/4+1/8+2*(1/16)) = 0

2 - (1/1+1/2+1/4+2*(1/8+)) = 0

4 - (2/1+1/1+1/2+2*(1/4)) = 0

... etc. , where the multiplication by 2 can be done in any wished place, which breaks the convergent series, in order to reach the value of the limit.

In other words, an infinite convergent series is found as long as it does not reach the value of the limit.

 

[jsfisher]

Here is the right way to get the value (and the concept) of Limit....

No, stop. Quit telling us about how others got it wrong. Quit drawing stupid pictures. Quit going off on tangents.

Focus, doron. Focus.

The task at hand is to explain how limits are defined in doronetics.

I know quite well how they work in Mathematics, and how they can be used to produce consistent and useful results. Now, how do you define limits in your little private world of OM?

...or will this be yet another thing you can't define, explain, or express in any consistent way?

 

[The Man]

Sum = accurate value

Inaccurate value ≠ Sum

Simple, isn't it?

Simply not true, is all it is.

We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy, for a multitude of purposes. You have never actually used math for anything (other than your fantasies) have you?

 

[doronshadmi]

Simply not true, is all it is.

We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy, for a multitude of purposes. You have never actually used math for anything (other than your fantasies) have you?

Let me help you.

There are at least two kinds of numbers under OM:

1) Local numbers that have accurate values.

2) Non-local numbers that do not have accurate values.

For example pi(= circumference/diameter) is a local number under OM.

3.14159265...[base 10] is a non-local number that does not have an accurate value.

No, stop. Quit telling us about how others got it wrong. Quit drawing stupid pictures. Quit going off on tangents.

Focus, doron. Focus.

The task at hand is to explain how limits are defined in doronetics.

I know quite well how they work in Mathematics, and how they can be used to produce consistent and useful results. Now, how do you define limits in your little private world of OM?

...or will this be yet another thing you can't define, explain, or express in any consistent way?

You may say that the limit of the non-local number 3.14159265...[base 10], is the local number pi, such that 3.14159265...[base 10] < pi.

By using this non-trivial notion, you may say that 3.14159265...[base 10] is similar to a virtual particle w.r.t to a non-virtual particle.

In other words, any local number is surrounded by non-local numbers, exactly as a non-virtual particle is surrounded by virtual particles.

 

[doronshadmi]

We can use estimated, rounded and even ranges of values to get sums with varying degrees of accuracy

In that case you do not distinguish, for example, between the accurate results of values like 3.1, 3.14, 3.141, 3.1415, 3.14159, ... ([base 10]) and the inaccurate result 3.14159...[base 10].

Non of these values above (accurate or inaccurate) are the accurate value pi(= circumference/diameter).

 

[sympathic]

Math as you know it works very good as a finite system, which has beautiful finite results.

If you wish to deal with the real complexity of the infinite, you first have to understand its qualitative atomic aspects which enables it, such that any infinite result of these aspects can't reach the completeness of the atomic quality.

In other words, approaches is an invariant property of any infinite complexity, such that w ≠ 0 and F(w) has no limit.

Infinite interpolation\extrapolation are valid concepts of the mathematical science, and they do not hide any behind the Limit-oriented curtain.

Your arrogance and confidence you have in the gibberish you write is just overwhelming. You haven't got a clue. In "real" math (not in Doron's fantasy math) infinity is a relative concept. In Statistics for example relatively small numbers (500 or even 30 in some cases) can be considered as infinity. Statistical theory as other branches of Math relies on limits.

You never learn and never will. How sad for you.

 

[doronshadmi]

In "real" math ... infinity is a relative concept.

If you ask Cantor he will tell you that infinity is an actual concept, which is not potential and not relative, because aleph0 is accurate exactly as 1 is accurate.

Sympathic you simply using words without any notion behind them, because you do not understand the real difference between infinite complexity which is relative, potential and inaccurate w.r.t the non-local and local atomic aspects, where non-locality is the actual infinity (notated as ∞) and locality is the actually finite (notated as 0).

By understanding the complex result of the linkage between the qualities of actual infinity (which is not the Cantorean actual infinity, which is a complex) and the actually finite, both Transfinite system and Infinitesimal system are changed by a paradigm-shift.

You may choose to work only under the standard paradigm, but this is your limited choice, not mine.

Your arrogance and confidence you have in the gibberish you write is just overwhelming.

Your Limit-oriented reasoning is underwhelming.

 

[sympathic]

If you ask Cantor he will tell you that infinity is an actual concept, which is not potential and not relative, because aleph0 is accurate exactly as 1 is accurate.

Sympathic you simply using words without any notion behind them, because you do not understand the real difference between infinite complexity which is relative, potential and inaccurate w.r.t the non-local and local atomic aspects, where non-locality is the actual infinity (notated as ∞) and locality is the actually finite (notated as 0).

By understanding the complex result of the linkage between the qualities of actual infinity (which is not the Cantorean actual infinity, which is a complex) and the actually finite, both Transfinite system and infinitesimal system are changed by a paradigm-shift.

You may choose to work only under the standard paradigm, but this is your limited choice, not mine.

I can't ask Cantor. He has been dead for nearly 92 years. Maybe you can through one of the uses of your direct perception. Even if I could I am sure this is not the answer I would get. His greatest accomplishment is perfectly aligned with what I have written. You refuse to learn anything from anyone but yourself - not a very productive approach.

 

[doronshadmi]

In Statistics for example relatively small numbers (500 or even 30 in some cases) can be considered as infinity. Statistical theory as other branches of Math relies on limits.

http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104

 

[sympathic]

http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104

How exactly is this related to what I wrote?

 

[doronshadmi]

I can't ask Cantor. He has been dead for nearly 92 years.

Really?? Thank you for this information (come on sympathic don't be lazy and look over the internet about Cantor and Actual infinity).

His greatest accomplishment is perfectly aligned with what I have written. You refuse to learn anything from anyone but yourself - not a very productive approach.

On the contrary, I distinguish between approach and reach. You can't, partially thanks to the Cantorean Transfinite system.

 

[doronshadmi]

How exactly is this related to what I wrote?

This part:

If one reaches the value of the limit, then one does not use an infinite convergent series, because in order to reach the limit's value one uses for example:

1 – (1/2+1/4+1/8+2*(1/16)) = 0

2 - (1/1+1/2+1/4+2*(1/8+)) = 0

4 - (2/1+1/1+1/2+2*(1/4)) = 0

... etc. , where the multiplication by 2 can be done in any wished place, which breaks the convergent series, in order to reach the value of the limit.

In other words, an infinite convergent series is found as long as it does not reach the value of the limit.

In order to understand it please read all of http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104.

 

[sympathic]

Really?? Thank you for this information (come on sympathic don't be lazy and look over the internet about Cantor and Actual infinity).


On the contrary, I distinguish between approach and reach. You can't, partially thanks to the Cantorean Transfinite system.

You don't get to tell me what I can or can't do.

 

[doronshadmi]

You don't get to tell me what I can or can't do.

You can't get OM.

You see? I can.

 

[zooterkin]

How exactly is this related to what I wrote?

In exactly the same way as OM relates to the real world.

 

[sympathic]

You can't get OM.

You see? I can.

I get what you do not. What you call OM is a mountain of gibberish spun out of a graphical representation of Integer partitions. Your futile attempts at driving more substance out of it are in vain.

 

[doronshadmi]

What you call OM is a mountain of gibberish spun out of a graphical representation of Integer partitions.

In other words, you don't get OM.