Cont: Deeper than primes - Continuation 2

[Kid Eager]

Strike three. I can now safely ignore the claims made by doronshadmi:
1. The claim is linguistic sophistry masking the inability to distinguish the map from the terrain (the terrain in this case being mathematics); and
2. Even were the claim valid, there is a fundamental inability to articulate the relevance of the claim and any consequence of the claim being true (or not)

I will no doubt be referred back to a previous post as being the claimed answer to my conclusions, but I now know that this is an avoidance tactic as none of the previous referenced links have answered the questions being asked.

Meanwhile, I'll stick around for the lulz (whilst acknowledging it is a bit sad that somebody is so emotionally wedded to a flawed idea).

Do carry on.

 

[doronshadmi]

The space between the braces is a space.

I basically use an unbounded (endlessly growing) 2-valued logical tree, and the meaning of space between the braces is contradiction.

We can use braces as a notational device in talking about sets and other things, but they have no significance beyond being an aid to communication. They certainly do not create meaning.

I basically use an unbounded (endlessly growing) 2-valued logical tree, and the meaning of the braces is contradiction.

You can choose to ignore it, but then you have nothing to criticize.

Also, your attempt to attribute some special meaning to a simple English word via the typographic equivalent of a pun fails.

The meaning is based exactly on an unbounded (endlessly growing) 2-valued logical tree, which means that it is independent of any particular language, English, Hebrew, Esperanto etc. ...

If you are hell-bent on introducing "NO thing" and "YES thing" into the terminology, go right ahead, but first you need to do something you have never done -- define them -- and if they are synonyms for existing terms, don't both, just use the existing terms.

They are defined logically by an unbounded (endlessly growing) 2-valued logical tree.

We do not need more than that in order to logically understand that, for example, {| |} < {|a,b,c|} < {|a,b,c,...|} < {|a,b,c,...|+1} < |{ }|.

-------------

In other words, you are simply missing www.internationalskeptics.com/forums/showpost.php?p=12331274&postcount=3019 , and this is exactly the reason why your reply is off topic.

Also make no mistake, my argument holds for any n-valued logical tree, such that n > 1 AND < ∞

 

[doronshadmi]

Some correction of the second sentence in the previous post.

It has to be:

I basically use an unbounded (endlessly growing) 2-valued logical tree, and the meaning of the braces is tautology.

 

[doronshadmi]

What is the disadvantage?

[of classic mathematics]

Unlike in classic mathematics, the cardinality of, for example, {a,b,c,...} (notated as {|a,b,c,...|} is endlessly changing (classic mathematics can't deal with non fixed cardinalities).

Yet it can be compared with other cardinal numbers, for example:

{|a,b,c,...|} < {|a,b,c,...|+1} by 1

{|a,b,c,...|} < {|a,b,c,...|*|a,b,c,...|} = {|a,b,c,...|*2} twice (in this case the notion of proportion is used).

etc.

Also {|a,b,c|} < {|a,b,c,...|} but the difference is non fixed.


Generally we have the following types of cardinality:

{| |} is the cardinality of NOthing (logically defined as contradiction). (classic mathematics can't deal with this notion)

|{ }| is the cardinality of YESthing (logically defined as tautology). (classic mathematics can't deal with this notion)


{|a,b,c|} is an example of a fixed cardinality (logically defined as ~contradiction AND ~tautology).

{|a,b,c,...|} is an example of a non fixed (endlessly changing) cardinality (logically defined as ~contradiction AND ~tautology). (classic mathematics can't deal with this notion)


The notion of proper subset, in case non fixed cardinality, is irrelevant. (classic mathematics can't deal with this notion)



thing in itself is the foundation of these types (including logic), which is not limited by them (it is not defined by its expressions, as illustrated, for example, by this logical structure). (classic mathematics can't deal with this notion)

-----------------------

Also see:

www.internationalskeptics.com/forums/showpost.php?p=12240674&postcount=2965

www.internationalskeptics.com/forums/showpost.php?p=12149738&postcount=2862

www.internationalskeptics.com/forums/showpost.php?p=12157394&postcount=2863

http://www.internationalskeptics.com/forums/showpost.php?p=12043625&postcount=2798

 

[Kid Eager]

[of classic mathematics]

Unlike in classic mathematics, the cardinality of, for example, {a,b,c,...} (notated as {|a,b,c,...|} is endlessly changing (classic mathematics can't deal with non fixed cardinalities).

Yet it can be compared with other cardinal numbers, for example:

{|a,b,c,...|} < {|a,b,c,...|+1} by 1

{|a,b,c,...|} < {|a,b,c,...|*|a,b,c,...|} = {|a,b,c,...|*2} twice (in this case the notion of proportion is used).

etc.

Also {|a,b,c|} < {|a,b,c,...|} but the difference is non fixed.


Generally we have the following types of cardinality:

{| |} is the cardinality of NOthing (logically defined as contradiction). (classic mathematics can't deal with this notion)

|{ }| is the cardinality of YESthing (logically defined as tautology). (classic mathematics can't deal with this notion)


{|a,b,c|} is an example of a fixed cardinality (logically defined as ~contradiction AND ~tautology).

{|a,b,c,...|} is an example of a non fixed (endlessly changing) cardinality (logically defined as ~contradiction AND ~tautology). (classic mathematics can't deal with this notion)


The notion of proper subset, in case non fixed cardinality, is irrelevant. (classic mathematics can't deal with this notion)



thing in itself is the foundation of these types (including logic), which is not limited by them (it is not defined by its expressions, as illustrated, for example, by this logical structure). (classic mathematics can't deal with this notion)

-----------------------

Also see:

www.internationalskeptics.com/forums/showpost.php?p=12240674&postcount=2965

www.internationalskeptics.com/forums/showpost.php?p=12149738&postcount=2862

www.internationalskeptics.com/forums/showpost.php?p=12157394&postcount=2863

http://www.internationalskeptics.com/forums/showpost.php?p=12043625&postcount=2798

*Sigh.* Here we go again. Great, you know how to re-state your claim, obtuse and problematic as it may be. Still waiting for the consequences.... no rush.

I can link to stuff too: https://arxiv.org/pdf/1204.2193.pdf

 

[doronshadmi]

Still waiting for the consequences....

Well, currently waiting is all what you do.

So this time please try to read www.internationalskeptics.com/forums/showpost.php?p=12334633&postcount=3024
(including it links) and ask concrete questions about their contents.

I can link to stuff too: https://arxiv.org/pdf/1204.2193.pdf

11.1.3 Continua and Points

A continuum is usually identified with the infinite set consisting of its points and the topology is captured as an additional structure given by metric or topological structure. In contrast we captured a continuum as a collection,

(page 142)


So Toru Tsujishita's work is still closed under the relativity of the notion of collection.

In my framework, continuum is non-composed (its cardinality is ∞ (www.internationalskeptics.com/forums/showpost.php?p=12331274&postcount=3019)).

 

[Kid Eager]

Well, currently waiting is all what you do.

So this time please try to read www.internationalskeptics.com/forums/showpost.php?p=12334633&postcount=3024
(including it links) and ask concrete questions about their contents.



(page 142)


So Toru Tsujishita's work is still closed under the relativity of the notion of collection.

In my framework, continuum is non-composed (its cardinality is ∞ (www.internationalskeptics.com/forums/showpost.php?p=12331274&postcount=3019)).

Been there, done that, read the links.

I was kinda hoping that you'd read Toru's paper and appreciate that you were out of your depth. Instead, you misunderstand it.

You're right - waiting is all I do, because you're unable to answer the question. It's been fun, but I can see that my earlier prediction has come true, so adieu.

 

[doronshadmi]

Been there, done that, read the links.

Kid Eager in order to show that you understand what you read, you have to replay to their contents by at least asking some questions, show some problems ect.

As long as you don't do that, the fact that you read them is still closed under waiting.

I was kinda hoping that you'd read Toru's paper and appreciate that you were out of your depth. Instead, you misunderstand it.

You did not show that you understand Toru's paper or my work, in order to claim that I misunderstand it.

On the contrary I show that Toru Tsujishita's work about the continuum is still closed under the relativity of the notion of collection (as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=12334736&postcount=3026) where in my framework, continuum is non-composed (its cardinality is ∞ (www.internationalskeptics.com/forums/showpost.php?p=12331274&postcount=3019)).

So, Kid Eager, not actually show that you understand Toru Tsujishita's work or my work, is equivalent to waiting.

Here are more links that are going to be added to your waiting list, as long as you do not reply to their contents (and also to Toru Tsujishita's work as well):

http://www.internationalskeptics.com/forums/showpost.php?p=12030522&postcount=2785

http://www.internationalskeptics.com/forums/showpost.php?p=12030765&postcount=2786

http://www.internationalskeptics.com/forums/showpost.php?p=12031447&postcount=2787

 

[doronshadmi]

The axiom of inaccessibility : "Given X, X is non-composed, such that it is above OR below Y".

An example:

Let A be a non-composed circle.

Let B be a point.

1/0 means that A is not composed by any amount of Bs, and therefore it is inaccessible from above by any amount of Bs on A (we are using the term "on" since A can't be defined in terms of collection of Bs).

1/n>0 means that any amount > 0 of Bs on A, is inaccessible from below to 0 Bs on A, which is again based of the fact that A is non-composed by any amount of Bs on A (again, A can't be defined in terms of collection of Bs).

So, the very notion of collection (represented here by points) is inaccessible to the non-composed (represented here by a non-composed circle) from below OR from above.

-----------------------

Let us focused on the case of inaccessibility from above.

In this case we are using the non-composed circle as a modular arithmetic framework in order to understand the concept of cardinality.

1/0 means that there is a non-composed modular arithmetic framework (represented here by numerator 1, where the denominator represents the amount of points on the domain of the non-composed modular arithmetic framework).

1/1 means that there is a single point on the non-composed modular arithmetic framework (by using the term "on" we mean that modular arithmetic framework is not composed by the points that are defined within its domain).

1/2 means that there are two points on the non-composed modular arithmetic framework.

1/… etc. ad infinitum.

Since no amount of points defines the non-composed modular arithmetic framework, the notion of transfinite cardinality as a fixed measurement value of infinitely many things (points, in this example) does not hold, since actual infinity is non-composed (beyond collections of infinitely many objects (points, in this example)).

So, the notion of the cardinality of all natural numbers as the smallest transfinite cardinal number (a fixed value named as ℵ₀) has no basis in terms of actual infinity.

 

[doronshadmi]

This post is based on the reasoning that actual infinity can't be defined in terms of collections (as observed in http://www.internationalskeptics.com/forums/showpost.php?p=12391433&postcount=3029).

-------------------

Intuitions of mathematicians, and the mathematics they develop, are ostensibly influenced by whether they primarily rely on visual_spatial and/or verbal_symbolic reasoning skills. Is it fair to say that mathematical activity of the majority of mathematicians for (at least) the past 300 years, was dominated by the use of their verbal_symbolic skills, and that this is reflected in the current body of mathematics?

-------------------

I wish to provide some examples that need your participation, in order to (I hope) understand better my question.

Please observe the first diagram by using both your visual_spatial AND verbal_symbolic reasoning skills:

Let X=1 (it actually can be any finite value > 0)

In that case:

The length of the black staircase = 2*(1/1) = 2

The length of the rad staircase = 4*(1/2) = 2

The length of the green staircase = 8*(1/4) = 2

The length of the purple staircase = 16*(1/8) = 2

The length of the blue staircase = 32*(1/16) = 2

The length of the cyan staircase = 64*(1/32) = 2

Etc. (there are infinitely many staircases with constant length 2).

-----------

Now, please observe the second diagram by using both your visual_spatial AND verbal_symbolic reasoning skills:

a=1/2 , b=1/4 , c=1/8 , d=1/16 , ...


By doing so the follow things are observed:


1) No infinitely many staircases with constant value 2 (for each staircase) are equal to √2 (the diagonal line) and this fact is written as 2>√2.

2) 2(a+b+c+d+...) is the result of the intersections of the diagonal black lines on the peaks of the infinitely many staircases, with the 2 sides of the diagram.

3) By (1) an (2) the convergent series 2(a+b+c+d+...)<2 exactly because (by using both your visual_spatial AND verbal_symbolic reasoning skills) it is inseparable of the fact that 2>√2.

4) By this inseparability 2(a+b+c+d+...) does not have an accurate sum (it has an accurate sum by persons that are using only their verbal_symbolic reasoning skills during their mathematical activity on this subject), but it has a non-accurate value < 2 (in case that it is observed by persons that are using both visual_spatial AND verbal_symbolic reasoning skills during their mathematical activity on this subject).

------

Here is the result of using only verbal_symbolic brain skills on the considered subject:

a=1/2 , b=1/4 , c=1/8 , d=1/16 , ...

S = 1/2 + 1/4 + 1/8 + 1/16 + ...

2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...

2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...) - S=(1/2 + 1/4 + 1/8 + 1/16 + ...) = S = 1

This result relies only on verbal_symbolic reasoning skills, and by doing so one is unaware that S<1 if observed by using visual_spatial AND verbal_symbolic reasoning skills (by this reasoning 2S<2 because S<1, so by subtracting S from 2S, one eliminates the fact (as observed by using visual_spatial AND verbal_symbolic reasoning skills) that S<1.

 

[MetalPig]

This again? Did you forget the last time you were corrected?

1) <...> this fact is written as 2>√2.

That should read: 2 >= √2


Therefore,

3) By (1) an (2) the convergent series 2(a+b+c+d+...)<2

should read :
the convergent series 2(a+b+c+d+...) <= 2



The sum is in fact equal to 2, so that's that.

 

[doronshadmi]

This again?

No, it is an improved version.

That should read: 2 >= √2

You actually wrote 2 > or = √2

I really wish to see the case where 2 = √2

 

[Hevneren]

This post is based on the reasoning that actual infinity can't be defined in terms of collections (as observed in http://www.internationalskeptics.com/forums/showpost.php?p=12391433&postcount=3029).

-------------------

Intuitions of mathematicians, and the mathematics they develop, are ostensibly influenced by whether they primarily rely on visual_spatial and/or verbal_symbolic reasoning skills. Is it fair to say that mathematical activity of the majority of mathematicians for (at least) the past 300 years, was dominated by the use of their verbal_symbolic skills, and that this is reflected in the current body of mathematics?

-------------------

I wish to provide some examples that need your participation, in order to (I hope) understand better my question.

Please observe the first diagram by using both your visual_spatial AND verbal_symbolic reasoning skills:


[qimg]http://c8.staticflickr.com//9//8463//28314892783_93fe8f577f_z.jpg[/qimg]

Let X=1 (it actually can be any finite value > 0)

In that case:

The length of the black staircase = 2*(1/1) = 2

The length of the rad staircase = 4*(1/2) = 2

The length of the green staircase = 8*(1/4) = 2

The length of the purple staircase = 16*(1/8) = 2

The length of the blue staircase = 32*(1/16) = 2

The length of the cyan staircase = 64*(1/32) = 2

Etc. (there are infinitely many staircases with constant length 2).

-----------

Now, please observe the second diagram by using both your visual_spatial AND verbal_symbolic reasoning skills:


[qimg]http://farm1.staticflickr.com/477/32803839331_d0a1bf1f9a_b.jpg[/qimg]

a=1/2 , b=1/4 , c=1/8 , d=1/16 , ...


By doing so the follow things are observed:


1) No infinitely many staircases with constant value 2 (for each staircase) are equal to √2 (the diagonal line) and this fact is written as 2>√2.

Brilliant. 2>√2. I agree.

2) 2(a+b+c+d+...) is the result of the intersections of the diagonal black lines on the peaks of the infinitely many staircases, with the 2 sides of the diagram.

OK.

3) By (1) an (2) the convergent series 2(a+b+c+d+...)<2 exactly because (by using both your visual_spatial AND verbal_symbolic reasoning skills) it is inseparable of the fact that 2>√2.

Doesn't follow.

4) By this inseparability 2(a+b+c+d+...) does not have an accurate sum (it has an accurate sum by persons that are using only their verbal_symbolic reasoning skills during their mathematical activity on this subject), but it has a non-accurate value < 2 (in case that it is observed by persons that are using both visual_spatial AND verbal_symbolic reasoning skills during their mathematical activity on this subject).

It does have an accurate sum. It's 2. Ask any mathematician.

------

Here is the result of using only verbal_symbolic brain skills on the considered subject:

a=1/2 , b=1/4 , c=1/8 , d=1/16 , ...

S = 1/2 + 1/4 + 1/8 + 1/16 + ...

2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...

2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...) - S=(1/2 + 1/4 + 1/8 + 1/16 + ...) = S = 1

This result relies only on verbal_symbolic reasoning skills, and by doing so one is unaware that S<1 if observed by using visual_spatial AND verbal_symbolic reasoning skills (by this reasoning 2S<2 because S<1, so by subtracting S from 2S, one eliminates the fact (as observed by using visual_spatial AND verbal_symbolic reasoning skills) that S<1.

My visual_spatial reasoning tells me that there's no gap at the end of the X line. And my verbal_symbolic skills confirms this. Sorry, but you just don't get even the simplest infinite series.

 

[zooterkin]

This post is based on the reasoning that actual infinity can't be defined in terms of collections

Since ‘collections’ are one of your (ill-defined) concepts, that is really only a problem for you.

 

[doronshadmi]

Brilliant. 2>√2. I agree.

My visual_spatial reasoning tells me that there's no gap at the end of the X line. And my verbal_symbolic skills confirms this. Sorry, but you just don't get even the simplest infinite series.

By actually using visual_spatial AND verbal_symbolic reasoning the fact that 2>√2 is inseparable of the fact that 2(a+b+c+d+...)<2.


In your case you are definitely using only your verbal_symbolic reasoning skills, exactly as shown at the last part of post http://www.internationalskeptics.com/forums/showpost.php?p=12404383&postcount=3030.

 

[doronshadmi]

Since ‘collections’ are one of your (ill-defined) concepts, that is really only a problem for you.

1) Please provide the well-defined mathematical definition of collections.

2) Please show that ‘collections’ are one of my (ill-defined) concepts.

 

[jsfisher]

This post is based on the reasoning ...

So, you are back to this, eh?

As much as you'd like to believe the staircase converges to the diagonal, it doesn't. Please stop repeating your same mistakes again and again.

 

[zooterkin]

1) Please provide the well-defined mathematical definition of collections.

Why on earth should I? You’re the one who keeps using the term without defining it.

 

[doronshadmi]

Why on earth should I? You’re the one who keeps using the term without defining it.

You wrote

Since ‘collections’ are one of your (ill-defined) concepts, that is really only a problem for you.

Ill-defined is not the same as not-defined, which means that your replies about the considered subject is undecidable by you.


Any way, by actually reading http://www.internationalskeptics.com/forums/showpost.php?p=12391433&postcount=3029 it is trivially understood that a collection is an aggregation of objects (where in http://www.internationalskeptics.com/forums/showpost.php?p=12391433&postcount=3029 the given objects are points on a non-composed circle, where the term "on" means that the given circle is not defined as a collection of points.

 

[doronshadmi]

As much as you'd like to believe the staircase converges to the diagonal, it doesn't.

You are missing my argument in http://www.internationalskeptics.com/forums/showpost.php?p=12404383&postcount=3030.

For example, Let X=1 (it can be any finite value > 0, but I use X=1 for the simplification of the discussion).

The fact that infinitely many staircases do not converge to the diagonal is given by 2>√2 that is inseparable of the fact that 2>2(a+b+c+d+...), where (a+b+c+d+...) is definitely converges.

This inseparability is known only by actually using visual_spatial AND verbal_symbolic reasoning.