Deeper than primes - Continuation

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Here is again my reply (without the typo mistakes) to the traditional mathematicians here:

Since the traditional mathematicians here are using only verbal_symbolic brain skills, thay can't understand that a set (the outer "{" "}") can't be a member of a given set.

In that case they can't comprehend the following theorem:
Being a set is different than being a member of a given set.

Moreover, they can't distinguish between a set, which is a collection of distinct objects, and a multiset, which is not a collection of distinct objects (the same object appears more than once as a member of a multiset).

These two inabilities are enough in order to ignore the rest of the traditional mathematicians' arguments, in this case, but look at the rest of their argument, which forces their enumerable infinity even if no mapping between the members of at least two sets, is involved in this theorem.

As for the universal set, since being a set is different than being a member of a given set, then no collection of members of a given set is extensible into the level of a given set, or in other words, no collection of members is complete with respect to the level of being a set, and the notion of strict transfinite cardinality is logically false.

Once again the traditional mathematicians here demonstrate how their conventions block their reasoning and do not allow them to get Cantor's Diagonalization in a non-traditional light.

You can look at the reply of the traditional mathematicians here to my theorem in http://www.internationalskeptics.com/forums/showpost.php?p=8448963&postcount=1673 (which uses Cantor's Diagonalization in a non-traditional way, such that no mapping is involved here) and also please look at their reply to what is quoted above.

You have to understand that the persons that accept or reject articles that are sent to professional mathematical journals, share the same "openness" about non-traditional works of already accepted mathematical frameworks.

So, the chance of non-traditional works of already accepted mathematical frameworks, to be accepted to, so called, important mathematical journals, is almost zero.

Any way, I air my view about my non-traditional mathematical ideas, whether I am considered as a mathematical crank by traditional mathematicians, or not, I really don't care.
 
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So, the set, S, is different from the lone member of the set, { S }. Doronetics is so wacky.
 
Any way, I air my view about my non-traditional mathematical ideas, whether I am considered as a mathematical crank by traditional mathematicians, or not, I really don't care.


Fear not, Doron. I, for one, do not consider you a true crank. Cranks, by and large, get most things right.
 
Now the traditional mathematicians here do not understand the difference between, for example, set S and set {S}, exactly because they do not understand the difference between being a set and being a member of a given set, which defines the difference between, for example, set S set {S}.

This misunderstanding is a natural result of verbal_symbolic-only reasoning, which keeps http://www.internationalskeptics.com/forums/showpost.php?p=8448963&postcount=1673 beyond the mind of the traditional mathematicians here ( for more details, please see the discussion on The set of all ideas at page 7 of http://www.scribd.com/doc/98276640/Umes ).
 
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Nope. Please go back and read the wiki article of the mathematical set.
Yep. In order to get verbal_symbolic AND visual_spatial reasoning, please notate the empty set, by using only its members.

After all you are the one who claims that "{ and } are not parts of the set."

So please support you claim, as mentioned above (and also please be aware of the fact that using ∅ is not identical to the members of the empty set).
 
You are not a passive factor in what I call The Organic Realm.

It means that you are a meaningful organ of that realm, which is aware of his responsibility to be an active participator of the development of this realm, where development is any harmonious AND consistent expression with the entire expressions of that realm.

Development needs a room in order to be expressed harmonically AND consistently, and this room is exactly the non-entropic conditions that are derived form the irreducibility of Membership into NOthing (that has no predecessor) AND the non-extensibility of Membership into YESthing (that has no successor).

In simpler words, verbal_symbolic AND visual_spatial brain skills are complement each other into a one unified formal reasoning, in order to provide the foundations of the unification among Ethical reasoning (in terms of evolutionary scale) AND Logical reasoning.

This unification can be done in each brain of self-aware creatures like us, where the survival of self-aware creatures is possible if it is developed into Unity-awareness.

The following verbal_symbolic AND visual_spatial expression demonstrates it:

Let's use a cross-section of Riemann sphere through its 0 and ∞ poles.

Doron, I asked you for a nonmathematical explanation on the middle school level of how your theory can improve my life. I didn't choose this goal for your theory; you did, as you've implied in the past that only by adopting your theory can we avoid destruction.

You come back with the above text? Putting aside the point it's completely incomprehensible in sections, what middle school did you go to, Doron?

The fact that you are unable to distill down your theory into comprehensible, easy to understand, pertinent information that any layman off the street can grasp and agree on it's importance tells me one of two things:

1) Your theory is useless, and / or
2) You don't yet have a deep enough understanding of it in order to make that leap towards comprehensibility.

The fact that you've been working on this for multiple years leads me to believe point #1.
 
Doron, I asked you for a nonmathematical explanation on the middle school level of how your theory can improve my life. I didn't choose this goal for your theory; you did, as you've implied in the past that only by adopting your theory can we avoid destruction.

You come back with the above text? Putting aside the point it's completely incomprehensible in sections, what middle school did you go to, Doron?

The fact that you are unable to distill down your theory into comprehensible, easy to understand, pertinent information that any layman off the street can grasp and agree on it's importance tells me one of two things:

1) Your theory is useless, and / or
2) You don't yet have a deep enough understanding of it in order to make that leap towards comprehensibility.

The fact that you've been working on this for multiple years leads me to believe point #1.

You wrote: "Don't use a single variable, don't use a single mathematical equation or concept above middle school level."

Well, I did not use a single variable, a single mathematical equation or concept above middle school level, exactly as you have asked.

3) You misinterpret the abilities of minds in middle school level, to understand the concepts used in my reply to you, before their minds are blocked by traditional mathematical experts.

4) You wrote: "I'm going to take it a step further:".
Well, you have missed the notion that "You are not a passive factor in what I call The Organic Realm.", or in other words, you did not take any step further in order to be an active participator instead of staying a passive observer (where a passive observer is still your current attitude about the considered subject).

The problem is not with middle school level, the problem is with traditional mathematical experts that, for example, can't comprehend that the difference between set S and set {S} is derived from the difference of being a set (for example, set S) and being a member of a given set (for example, set {S}) (look what they have done to the mind of Little 10 Toes).

This misunderstanding prevents the importance of non-entropic conditions for further development of creatures like us (as clearly shown in the discussion on The set of all ideas at page 7 of http://www.scribd.com/doc/98276640/Umes).
 
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Yep. In order to get verbal_symbolic AND visual_spatial reasoning, please notate the empty set, by using only its members.

After all you are the one who claims that "{ and } are not parts of the set."

So please support you claim, as mentioned above (and also please be aware of the fact that using ∅ is not identical to the members of the empty set).

Can you show me where { and } are part of the set? Somewhere independent of yourself, your "works" and this website please? Your claim, your burden of proof.

I'll be glad to support my claim even though you have not supported your claim that { and } are parts of the set. You got called on your claim and you never have produced any proof than "because I say so".

Did you follow *any* of the links I showed you. There were only 2. I even told you where to go and what to look for. I guess I need to help you even further.

http://en.wikipedia.org/wiki/Set_(mathematics)#Describing_sets said:
Describing sets

There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description:

A is the set whose members are the first four positive integers.
B is the set of colors of the French flag.​

The second way is by extension – that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets:
C = {4, 2, 1, 3}
D = {blue, white, red}.​

*internal links removed

There are "members of the empty set" (bolding added)? Where did you get that idea? If a set has members, it's not empty now, is it? How about listing all the members of the empty set, according to you.

The empty set is just that, empty. For example, the set of nuclear powered vehicles that I own is empty. Please note that I am not asking for the number of vehicles, but just the vehicles themselves. I can then list the set two ways, either by {} or by ∅.

Why {} or ∅, you may ask. Way ahead of you.
http://en.wikipedia.org/wiki/Empty_set said:
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

*internal links removed
http://en.wikipedia.org/wiki/Empty_set#Notation said:
Common notations for the empty set include "{},"∅", and " ". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabet (and not related in any way to the Greek letter Φ).

*internal links removed
Please note that the third common notation has an image in it. The best way to describe the notation is to take the 2nd notation and make it tall and skinny.
 
Let's see:

{ and } are not parts of the set.
Can you show me where { and } are part of the set?

I can then list the set two ways, either by {} or by ∅.
So after all, you are using the outer "{" "}" as a notation that describes the thing called Set (whether it is empty, or not, for example: S={} or S=∅ or S={{}} or S={x} or S={x,...} etc., where in all cases the notation of the thing called Set is beyond the existence of a given member (or its absence, in the case of S={} or S=∅)).

Now what is left for you is to be aware of your own answer.

Can you do this trick?

If not, you are categorized as a non self-aware phenomenon (exactly as the traditional mathematicians here) of the considered subject.
 
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So after all, you are using the outer "{" "}" as a notation that describes the thing called Set (whether it is empty, or not, for example: S={} or S=∅ or S={{}} or S={x} or S={x,...} etc., where in all cases the notation of the thing called Set is beyond the existence of a given member (or its absence, in the case of S={} or S=∅)).


The confusion is strong in this Padawan.
 
The traditional black Jedi knights here are known by their non self-awareness ( http://www.youtube.com/watch?v=-ZoD9uXhl3w ).

After all, Mathematics for the traditional mathematicians here is mechanic (also called formal) game, where the mathematician's awareness is not a factor (does not have any influence, on the, so called, platonic realm reports) of this game.

Such an attitude is the foundation of the non-responsibility that characterizes the formal education of traditional mathematicians, especially the "pure" one.

Organic Mathematics' aim is to reduce the influence of this non-responsible mechanic formal education that was developed for the past 4000 years, and transform it into a framework that consistently enables to unify Ethical reasoning (in terms of evolutionary scale) AND Logical reasoning.

It can't be done, as long as the mathematical science in known as a mechanic (also called formal) game, where the mathematician's awareness is not a factor (does not have any influence, on the, so called, platonic realm reports) of this game (which is characterized by the built-in non-responsibility of its educational training, exactly because the trained mind learns how not to be a factor of this science, in order to develop his\her platonic realm reports).

PiedPiper, I hope that this post can help you to understand better my replies to you in http://www.internationalskeptics.com/forums/showpost.php?p=8451753&postcount=1689 and http://www.internationalskeptics.com/forums/showpost.php?p=8449731&postcount=1679.
 
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Let me write my theorem and proof again, by adding some remarks that may help to understand my non-traditional use of Cantor's Diagonalization and its implications on the validity of the transfinite universe:

A set is a collection of distinct members (which is different than a multiset, that can have the same member more than once), and this definition (of being a collection of distinct members) is not changed even if we deal with infinitely many degrees of powers of sets.

Theorem:

Being a set is different than being a member of a given set.

Proof:

(1) Let us suppose that being a set is the same as being a member of a given set.

(2) Every member of a given set is different than the other members of that set.

(3) According to (2) each member can be represented by a unique code, where in the case of infinite collection of members there is no first or last code, where each unique code is an infinitely long sequence of symbols without first or last symbol, for example:

{
...

...01001... ,
...11101... ,
...10110... ,
...11111... ,
...10101... ,
...

}

(4) The code of a set is defined by using Cantor's Diagonalization (without using any mapping between the members of two given sets), which is different than the other codes that represent its members (in this example the code of a given set is ...10000...).

(In order to get a unique Cantor's Diagonalization code (in case that there is no first or last code, and also each code does not have first or last symbol) we arbitrarily choose some symbol of some arbitrary distinct code, and from there (by including the arbitrarily chosen symbol) we construct a complement "0;1" code by "moving" simultaneously from the arbitrarily chosen symbol infinitely many times (up AND left) AND (down AND right) by single steps).

(5) If a set is one of its own members, then its code (for example:...10000...) must appear in the collection of the unique codes, which represent the members of that set.

(6) But according to (4) the code of a set is defined by using Cantor's Diagonalization (without using any mapping between the members of two given sets), and in this case the code that represents a given set is different than the codes that represent the members of a given set (the example ...10000... can't be considered as the code of a given set, if it is used to represent a member of that set, because if ...10000... is added as one of the codes that represent some member of that set, Cantor's Diagonalization code that represents the set, is changed, etc. ad infinitum).

(7) According to (6) assumption (1) is false and we can conclude that being a set is different than being a member of a given set.

Q.E.D

The implication of this proof is that no amount of collection of infinitely many distinct members has a strict cardinality, or in other words, the transfinite universe is logically a false assumption.

Prof. Kauffman used Flagg resolution such that:
Code:
 J = ...010101010101010101010101010...
~J = ...101010101010101010101010101...

I show that Flagg resolution is actually a particular case of some member's code and some complement set's code that is defined by using Cantor's Diagonalization (without using any mapping between the members of two given sets).

For example, code ...01111... represents a given member, and code ...10000... represents a given set, where Cantor's Diagonalization (without using any mapping between the members of two given sets) guarantees the difference between the code that represents a set, and the code that represents a member of a given set, such that no amount of collection of infinitely many unique codes, has a strict cardinality, or in other words, Cantor's transfinite universe does not hold.
 
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Too bad doronshadmi can't answer direct challenges.

I never said {} describes a set. You did.

Yes, you did:
Little 10 Toes said:
I can then list the set two ways, either by {} or by ∅.
but you are still unaware of it, like any traditional mathematician here.

Let's try again, please notate the empty set by using only its members.

If you can do that, I agree with you the the outer "{" and "}" has nothing to do with set.
 
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Yes, you did:

but you are still unaware of it, like any traditional mathematician.

Let's try again, please notate the empty set by using its members.

If you can do that, I agree with you the the outer "{" and "}" has nothing to do with set.

Is your English comprehension so poor that you don't understand the difference between "list" and "describe". For example, give me a list of internal organs. Does that describe an animal?

Here's a list of questions/statement/requests that you have not responded to:

  • Can you show me where { and } are part of the set? Somewhere independent of yourself, your "works" and this website please? Your claim, your burden of proof.
  • There are "members of the empty set" (bolding added)? How about listing all the members of the empty set, according to you.

Here's the members of the empty set:
 
Let me write my theorem and proof again, by adding some remarks that may help to understand my non-traditional use of Cantor's Diagonalization and its implications on the validity of the transfinite universe:

A set is a collection of distinct members (which is different than a multiset, that can have the same member more than once), and this definition (of being a collection of distinct members) is not changed even if we deal with infinitely many degrees of powers of sets.

You insistence to throw in extra qualifiers isn't particularly helpful, Doron. Usually they are just redundant or meaningless; here, though, it is wrong. In Set Theory, there is no requirement for "distinct members" simply because Set Theory provides no means to tell if any member appears more than once. The sets, {a} and {a,a,a,a,a,a,a}, are indistinguishable from each other, but they are both valid sets.

Theorem:

Being a set is different than being a member of a given set.

Your theorem statement remains false, just on the face of it. The same counterexample disproves it. It is as if you'd said "being a positive integer is different from being a factor of a positive integer." All positive integers are factors of positive integers; all sets are members of sets.

What did you really mean to say?



The entirety of your "proof" continues to be nonsense, too, but since you fail at the theorem statement, we can stop there.
 
Actually, I did answer your question. The empty set has no members.
Yet the empty set is not identical to nothing, since a set (empty or not) is an existing thing (whether existence is taken as an abstract or non-abstract concept).

Do you understand the implications of what I wrote above?
 
You wrote: "Don't use a single variable, don't use a single mathematical equation or concept above middle school level."

Well, I did not use a single variable, a single mathematical equation or concept above middle school level, exactly as you have asked.

3) You misinterpret the abilities of minds in middle school level, to understand the concepts used in my reply to you, before their minds are blocked by traditional mathematical experts.

4) You wrote: "I'm going to take it a step further:".
Well, you have missed the notion that "You are not a passive factor in what I call The Organic Realm.", or in other words, you did not take any step further in order to be an active participator instead of staying a passive observer (where a passive observer is still your current attitude about the considered subject).

The problem is not with middle school level, the problem is with traditional mathematical experts that, for example, can't comprehend that the difference between set S and set {S} is derived from the difference of being a set (for example, set S) and being a member of a given set (for example, set {S}) (look what they have done to the mind of Little 10 Toes).

This misunderstanding prevents the importance of non-entropic conditions for further development of creatures like us (as clearly shown in the discussion on The set of all ideas at page 7 of http://www.scribd.com/doc/98276640/Umes).

Not only did you not give me an example of how this directly impacts upon / improves my life, it's now obvious to me that you can't put your theory in simple terms. No-one speaks like you do in everyday, conversational English, Doron. Communication is key in science - all science. It's no wonder you've been beating your head against a wall and facing so much opposition.

How about this: put your "theory" in the simplest possible terms. Absolutely the simplest possible terms. Then tell me why it's important, and why I should pay attention. Because all I see at the moment is a bunch of "poo-pooing" those who "don't get" it as well as a bunch of made-up phrases that I've not seen outside this thread, posted by you.

Balls in your court, Doron...
 
Here's a thought question for Doron:

How do you distinguish between ...110111... and ...111011...? Are the sequences the same or different? Is the question even meaningful?

You should assume the two sequences extend without bound with 1's to both the left and the right.
 
Not only did you not give me an example of how this directly impacts upon / improves my life, it's now obvious to me that you can't put your theory in simple terms. No-one speaks like you do in everyday, conversational English, Doron. Communication is key in science - all science. It's no wonder you've been beating your head against a wall and facing so much opposition.

How about this: put your "theory" in the simplest possible terms. Absolutely the simplest possible terms. Then tell me why it's important, and why I should pay attention. Because all I see at the moment is a bunch of "poo-pooing" those who "don't get" it as well as a bunch of made-up phrases that I've not seen outside this thread, posted by you.

Balls in your court, Doron...

http://67.228.115.45/showpost.php?p=8452050&postcount=1694
 
{a} and {a,a,a,a,a} are mathematical objects, where {a} is an example of a set and {a,a,a,a,a} is an example of a multiset.

In traditional set theory {a} = {a,a,a,a,a} such that {a,a,a,a,a} is reduced into {a} and the cardinality of {a} = 1.

In both cases the objects are considered as sets or multisets only if the outer "{" and "}" are used.
 
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In traditional set theory {a} = {a,a,a,a,a} such that {a,a,a,a,a} is reduced into {a} and the cardinality of {a} = 1.


Really? Let's stick to ZFC as our reference model. Just where in ZFC can {a,a,a,a,a} be reduced into {a}? Answer: nowhere. In ZFC, the two sets are indistinguishable. There is no test that can be applied to tell them apart. So, {a} = {a,a,a,a,a} (without having to be "reduced"), and, yes, |{a}| = |{a,a,a,a,a}|.



Doron, you really need to let go of the gross simplifications you learned in elementary school. Mathematics is much more precise, elegant, and beautiful than your sloppy, misleading concepts allow you to experience.
 
The traditional mathematicians here can't get the distinct "0;1" sequences along a binary tree, which is unbounded above AND unbounded below.

Q: How do we know that they can't get such a tree?

A: Because they can't get the difference between two unbounded "0;1" sequences that binary tree, such that the two sequences share the same levels along that binary tree, but they do not share the same symbols in each given level of that binary tree, for example:
Code:
Levels = ... -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3 ...

Seq_a =  ...  1  1  1  1  0  1  1  1  1  1  1  1 ...

Seq_b =  ...  1  1  1  1  1  1  1  0  1  1  1  1 ...

In other words, they are two different sequences of the same unbounded binary tree.
 
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Oh, isn't that cute. This is posed to Doron:

How do you distinguish between ...110111... and ...111011...? Are the sequences the same or different? Is the question even meaningful?


and Doron wanders off to blather on about binary trees.

The traditional mathematicians here can't get the distinct "0;1" sequences along a binary tree


Ok, let's accept your binary tree excursion. How did you decide where it was rooted? There is nothing, absolutely nothing, in the original question to justify you selecting any element in the sequence as your root.

That's the whole point of the question, by the way. There is no way to distinguish between the two sequences without an additional assumption well beyond the problem statement.
 
A question to a traditional mathematician:

Since {a} and {a,a,a,a,a} are indistinguishable, then what is the value of X, such that X = |{a}| = |{a,a,a,a,a}|?
 
The traditional mathematicians here still can't get the distinct "0;1" sequences along a binary tree, which is unbounded above AND unbounded below, because they are totally ignore http://www.internationalskeptics.com/forums/showpost.php?p=8454935&postcount=1711.

Please do not expect to much from minds that were trained for many years not to use their awareness as a factor of some mathematical research.
 
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A question to a traditional mathematician:

Since {a} and {a,a,a,a,a} are indistinguishable, then what is the value of X, such that X = |{a}| = |{a,a,a,a,a}|?


As Cantor observed in his work, cardinality in its basic form in Set Theory is a relative measure. Less than, greater than, and equal to. The cardinality of {a} and {a,a,a,a,a}, those being indistinguishable sets, are equal.

If you want to extend cardinality to have numeric values (at least for finite sets), that is normally done by interpreting the induction set as the set of integers, mapping a set to a subset of the induction set, and so on. Under that extension (which brings the term, cardinality, more in line with the myth you may have learned in elementary school), then the cardinality of {a} is 1, as is the cardinality of {a,a,a,a,a}.

Again, set theory provides no way to determine how many of an element are in a set, only whether it is in the set.

The traditional mathematicians here still can't get the distinct "0;1" sequences along a binary tree, which is unbounded above AND unbounded below, because they are totally ignore http://www.internationalskeptics.com/forums/showpost.php?p=8454935&postcount=1711.

Please do not expect to much from minds that were trained for many years not to use their awareness as a factor of some mathematical research.

Ignoring my question, I see. How do you establish the root of whatever binary tree you think is involved? The truth is you do not have any effective means to establish the root, and so you have no effective means to distinguish among, say, ...111011... and ...110111... and ...1111111011111....

As is you style, when backed into a corner with facts you resort to silly name-calling and pointers back to inane, irrelevant posts.
 
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Meanwhile, we still have this bit of nonsense:
Theorem:

Being a set is different than being a member of a given set.


Seriously, Doron, did you mean to say, "No set is a member of itself"? What you wrote doesn't, and if that's what you really meant, why not just say it that way? Here, I'll help. Just copy and paste this:

Theorem: [i]No set is a member of itself.[/i]​
 
I still fail to see how this is important to my life or why I should pay attention. I've read everything you've shown to me and viewed every post directed at me. I'm not a mathematician.

Can you - is it within your capability - to tell me how your theory is going to change my life for the better? Or is that not possible? If it's not possible, I'll leave this thread to the likes of others who seem to enjoy arguing obstruse aspects of set theory with you.
 
Actually, I did answer your question. The empty set has no members.

So you did not succeed to answer my questions.

Do you know why you have failed to do that?

Yet the empty set is not identical to nothing, since a set (empty or not) is an existing thing (whether existence is taken as an abstract or non-abstract concept).

Do you understand the implications of what I wrote above?

You're correct. A set is something. The empty set (as a whole) is something, however, the empty set contains nothing in it.

By the way, I guess you can't prove that the empty set has members and that { and } are part of a set. Kudos for me for winning those points.
 
You're correct. A set is something. The empty set (as a whole) is something, however, the empty set contains nothing in it.

By the way, I guess you can't prove that the empty set has members and that { and } are part of a set. Kudos for me for winning those points.


Stock "You don't get it" reply accompanied by insult and a reference to a previous irrelevant post in 5...4...3...
 
I still fail to see how this is important to my life or why I should pay attention. I've read everything you've shown to me and viewed every post directed at me. I'm not a mathematician.

Can you - is it within your capability - to tell me how your theory is going to change my life for the better? Or is that not possible? If it's not possible, I'll leave this thread to the likes of others who seem to enjoy arguing obstruse aspects of set theory with you.

To simplify doronshadmi's answer, the theory is good for nothing because he can't prove it's good for anything. It hasn't produced anything of value for others as well.
 
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