Deeper than primes - Continuation

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zooterkin said:
Firstly, no, the elements stand for themselves, not other things. Secondly, what other options?
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EDIT:

1) It is nothing by your decision.

2) Also by following your decision the following definition of powerset holds:

Let's improve again the more general definition of powersets,

A powerset P(S) is (a collection of 2^|S| distinguished elements, which are defined by collections with |S| distinguished elements, which share the same type of form with the distinguished elements of P(S)) OR (the elements of P(S) are constructed by the elements of a given S and the empty set is one of its distinct elements).

According to this definition cases like {0,6,@,!}{6,%} are avoided.

The second part of the more general definition (after the OR logical condition) is actually the traditional definition, but now the traditional definition is not the only option to define the concept of powerset.

Some examples are shown in http://www.internationalskeptics.com/forums/showpost.php?p=8165288&postcount=1069
 
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doronshadmi said:
Let's improve again the general definition of powersets
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No, thank you. You maim rather than improve. The axiom of power set is just fine exactly the way it is:

[latex]$$$\forall S \, \exists P \, \forall A \, [A \in P \iff \forall B \, (B \in A \Rightarrow B \in S)]$$$[/latex]​

where S is any set (including the empty set, which, for some reason, you always seem to exclude), and P is its power set.

If you wish to continue to cripple Doronetics, knock yourself out, but leave the stuff the works alone.
 
doronshadmi said:
As shown in http://www.internationalskeptics.com/forums/showpost.php?p=8168019&postcount=1121 , the traditional definition of powerset is nothing but some option of more general definition, that enables to conclude things ( as shown in http://www.internationalskeptics.com/forums/showpost.php?p=8165288&postcount=1069 ) that can't be achieved by the traditional definition.
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That's ok. The whole point is for it to not include things that "can't be achieved by the traditional definition." The traditional definition has proven itself quite useful over the years. Real math continues to get real results. Disfigure and neuter Doronetics any way you like, because it doesn't look like it will ever turn useful, but leave the stuff that works alone.
 
It is lovely to see how a traditional mind ignores anything that does not fit its traditional framework, which is actually the result of decisions of a traditional mind.
 
doronshadmi said:
The traditional definition of powerset is not well-defined, because it leads to unnecessary limitations of this concept.
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It is quite well defined. There are no unnecessary limitations.

Here's the definition from wikipedia: In mathematics, the power set (or powerset) of any set S, written , P(S), ℘(S) or 2S, is the set of all subsets of S, including the empty set and S itself.

Notice how it is written using superscript.
 
doronshadmi said:
It is lovely to see how a traditional mind ignores anything that does not fit its traditional framework, which is actually the result of decisions of a traditional mind.
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I notice you continue to ignore requests to show what you can do with Doronetics that can't be done with 'traditional' maths (leaving aside the fact that you probably can't even do the same things).
 
Little 10 Toes said:
It is quite well defined. There are no unnecessary limitations.

Here's the definition from wikipedia: In mathematics, the power set (or powerset) of any set S, written , P(S), ℘(S) or 2S, is the set of all subsets of S, including the empty set and S itself.

Notice how it is written using superscript.
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Very nice, now please read http://www.internationalskeptics.com/forums/showpost.php?p=8168147&postcount=1123 including the links that are found in these posts.
 
doronshadmi said:
It is lovely to see how a traditional mind ignores anything that does not fit its traditional framework, which is actually the result of decisions of a traditional mind.
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For about 3 years now we have not ignored your ramblings and misquotations, even though they do not fit into any consistent framework.

Neither your own, nor traditional mathematic frameworks can hold, or prove your disheveled heap of loose exclamations.

You never ever, not even once, not in any of the previous posts (and you probably will post a link or two or more to 'prove' something that is not proven in those posts, only misquoted, mangled or otherwise wrongly stated) that Doronetics can do 1 single thing that traditional frameworks can not.

You do NOT have a beautiful mind and all you produce is so ugly only it's own father could love.

The whole above story is typical of your 'mathematical prowess'; you make a claim:

'No set is complete.'

Then ramble along with things like:

'Powerset blabbla, look at that specific sentence in wikipedia' (buy some real math books).

And when proven wrong (both in idiomatic and axiomatic ways) to cop out with:

'But I never meant it to be to be traditional, your minds are all soooo traditional.'

Ending with another pilpul on:

'When I call it a powerset it is the improved version I did not tell anyone yet about. It has the magical unicorn properties that make my statements true and yours not. I can not ever be wrong, because my mind is like the mind of the guy in the moooooviiieee, and you are all so traditional. Really.'

For the umpteenth time:

Show something that Doronetics can do which traditional math can not.
And so as not to get in to another nowhere with you, can you mark each axiom, lemma or conclusion with a sign that says 'Doron Maths (DM)' or 'Traditional Maths (TM)'?
 
realpaladin said:
For about 3 years now we have not ignored your ramblings and misquotations, even though they do not fit into any consistent framework.

Neither your own, nor traditional mathematic frameworks can hold, or prove your disheveled heap of loose exclamations.

You never ever, not even once, not in any of the previous posts (and you probably will post a link or two or more to 'prove' something that is not proven in those posts, only misquoted, mangled or otherwise wrongly stated) that Doronetics can do 1 single thing that traditional frameworks can not.

You do NOT have a beautiful mind and all you produce is so ugly only it's own father could love.

The whole above story is typical of your 'mathematical prowess'; you make a claim:

'No set is complete.'

Then ramble along with things like:

'Powerset blabbla, look at that specific sentence in wikipedia' (buy some real math books).

And when proven wrong (both in idiomatic and axiomatic ways) to cop out with:

'But I never meant it to be to be traditional, your minds are all soooo traditional.'

Ending with another pilpul on:

'When I call it a powerset it is the improved version I did not tell anyone yet about. It has the magical unicorn properties that make my statements true and yours not. I can not ever be wrong, because my mind is like the mind of the guy in the moooooviiieee, and you are all so traditional. Really.'

For the umpteenth time:

Show something that Doronetics can do which traditional math can not.
And so as not to get in to another nowhere with you, can you mark each axiom, lemma or conclusion with a sign that says 'Doron Maths (DM)' or 'Traditional Maths (TM)'?
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Ok you spited it out, now please read http://www.internationalskeptics.com/forums/showpost.php?p=8168147&postcount=1123 including the links that are found in these posts.
 
doronshadmi said:
I notice that you ignore http://www.internationalskeptics.com/forums/showpost.php?p=8168147&postcount=1123 .
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I apologise that I was not as clear as I should have been; clearly, with Doronetics you can waste a lot of time and generate meaningless strings of symbols. Let me rephrase slightly:

I notice you continue to ignore requests to show what you can do that is useful with Doronetics that can't be done with 'traditional' maths (leaving aside the fact that you probably can't even do the same things).
 
doronshadmi said:
Ok you spited it out, now please read http://www.internationalskeptics.com/forums/showpost.php?p=8168147&postcount=1123 including the links that are found in these posts.
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For the people that do not want to follow the 'linkstringing' tactic that Doron uses so people do not read the counter arguments:

The pages are:

http://www.internationalskeptics.com/forums/showthread.php?t=221845&page=23 -> You fail to answer the most basic questions about a formula that is hugely visible to everyone.

http://www.internationalskeptics.com/forums/showthread.php?t=221845&page=22 -> Where you fall flat on your face with regards to what you mention on this page.

As anyone can see, the links you point to are nothing but a tactic to avoid answering and/or reacting to proper logical reasoning.

So, again... Doron, in *all* of these links, you have *completely* nothing to show for.
 
Little 10 Toes said:
Prove it.

Edit: Nice edit. You claimed I did not read the post.
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That is why Zooterkin and me sometimes just quickly quote Doron when he posts... it is known to happen that he changes his direction in midflight or even after having seen answers from others.

His tactic of linkstringing has brought me almost to the point where I am willing to make a 'Doron proxy' so it shows the whole thread and not his selected links.
 
zooterkin said:
I apologise that I was not as clear as I should have been; clearly, with Doronetics you can waste a lot of time and generate meaningless strings of symbols. Let me rephrase slightly:

I notice you continue to ignore requests to show what you can do that is useful with Doronetics that can't be done with 'traditional' maths (leaving aside the fact that you probably can't even do the same things).
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The understanding that no collection is complete, is very useful for the understanding of Entropy and the understanding of the power of the continuum.

Since no collection has the power of the continuum, we are actually living in a non-entropic realm (a naturally open realm), which always have a room for further development.

This understanding can't be achieved by using Traditional Maths, because any given thing is already complete (there is no room for further development).
 
doronshadmi said:
The understanding that no collection is complete, is very useful for the understanding of Entropy and the understanding of the power of the continuum.

Since no collection has the power of the continuum, we are actually living in a non-entropic realm (a naturally open realm), which always have a room for further development.

This understanding can't be achieved by using Traditional Maths, because any given thing is already complete (there is no room for further development).
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But your understanding is wrong. Again, if I have a collection (or a set) of the English single digit signed numbers when spelled out have exactly 4 letters is {four, five, nine}, my set is complete.

Please show where my collection is incomplete.
 
realpaladin said:
For the people that do not want to follow the 'linkstringing' tactic that Doron uses so people do not read the counter arguments:

The pages are:

http://www.internationalskeptics.com/forums/showthread.php?t=221845&page=23 -> You fail to answer the most basic questions about a formula that is hugely visible to everyone.

http://www.internationalskeptics.com/forums/showthread.php?t=221845&page=22 -> Where you fall flat on your face with regards to what you mention on this page.

As anyone can see, the links you point to are nothing but a tactic to avoid answering and/or reacting to proper logical reasoning.

So, again... Doron, in *all* of these links, you have *completely* nothing to show for.
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Wrong. http://www.internationalskeptics.com/forums/showpost.php?p=8168147&postcount=1123 including the links that are found in these posts, is exactly my answer.
 
doronshadmi said:
The understanding that no collection is complete, is very useful for the understanding of Entropy and the understanding of the power of the continuum.
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Why and how?

doronshadmi said:
Since no collection has the power of the continuum, we are actually living in a non-entropic realm (a naturally open realm), which always have a room for further development.
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From an alleged 'no collection has the power of the continuum' you jump to 'we are *actually* living in a non-entropic realm'.

That really needs more work.

- You can not and have not proven yet that NO collection is complete.
- You have not proven the existence of a continuum.
- You have not proven any causal relation between the notion 'collections' and reality.
- You have not shown that incomplete collections must mean a non-entropic realm.

doronshadmi said:
This understanding can't be achieved by using Traditional Maths, because any given thing is already complete (there is no room for further development).
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Then, what is the final digit of the decimal representation of Pi? The formulaic description is exact, but as I recall, the decimal number is never complete.
 
Little 10 Toes said:
But your understanding is wrong. Again, if I have a collection (or a set) of the English single digit signed numbers when spelled out have exactly 4 letters is {four, five, nine}, my set is complete.

Please show where my collection is incomplete.
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If you look at http://www.internationalskeptics.com/forums/showpost.php?p=8163493&postcount=1052 you can understand how to translate your set with 3 distinct elements, into the more general form of 3 bits that are represented by 0;1 symbols.

By doing that you are able to use Diagonalization among the 3 elements (with 3 bits each) of each given set and conclude that it is incomplete, exactly because you are able to define an explicit element of that form, which is not an element of that set.

Things do not change even if infinitely many sets with infinite amount of elements (where each element has infinitely many bits) are involved.

In other words, try to think abstract.
 
realpaladin said:
Then, what is the final digit of the decimal representation of Pi? The formulaic description is exact, but as I recall, the decimal number is never complete.
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Good, you start to get it, The formulaic description is like a line that can't completely be covered by the symbols of the decimal expression (where the symbols are like points).

The expressions of a given rule are not completely express the rule (there is always a room for more expressions of that rule, or in other words, we are dealing with a non-entropic framework).
 
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doronshadmi said:
Good, you start to get it, The formulaic description is like a line that can't completely be covered by the symbols of the decimal expression (where the symbols are like points).
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So, you admitted to incompleteness in Traditional Math. But just a few posts earlier you said it was not possible....
 
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doronshadmi said:
If you look at http://www.internationalskeptics.com/forums/showpost.php?p=8163493&postcount=1052 you can understand how to translate your set with 3 distinct elements, into the more general form of 3 bits that are represented by 0;1 symbols.

By doing that you are able to use Diagonalization among the 3 elements (with 3 bits each) of each given set and conclude that it is incomplete, exactly because you are able to define an explicit element of that form, which is not an element of that set.

Things do not change even if infinitely many sets with infinite amount of elements (where each element has infinitely many bits) are involved.

In other words, try to think abstract.
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Why are you trying to complicate things? Why do I need to convert my elements into binary? Let me list to you the power set of my set: { {null}, {four}, {five}, {nine}, {four, five}, {four, nine}, {five, nine}, {four, five, nine} }. Not that hard. Where is my incompleteness. My original set is complete and so is my powerset.
 
doronshadmi said:
The expressions of a given rule are not completely express the rule (there is always a room for more expressions of that rule, or in other words, we are dealing with a non-entropic framework).
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So you admit that Doronetics can not do anything Traditional Math can not do as well?

Good for you!
 
realpaladin said:
So, you admitted to incompleteness in Traditional Math. But just a few posts earlier you said it was not possible....
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Well I am more like a mirror in front of your mind, but you still do not recognize your reflection in it.
 
doronshadmi said:
No, the incompleteness is not shown by using only Traditional Math.
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So then you admit that Traditional Maths is correct in the context of Traditional Maths and that your work has nothing to do with Traditional Maths.

And it took you only 3 years... lightning! Good for you!
 
Little 10 Toes said:
So only by using your terms/definitions (which constantly change and/or cannot be defined clearly), and buy using your plan (which has no improvements over current math) can you show something (which only you claim is important).
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And even then it is wrong. Try reversing the Doronetics results to find out which element you are missing. It probably is octarine.
 
doronshadmi said:
Worng, Traditional Maths is context-dependent-only framework of closed (and therefore entropic) systems.
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That is a statement that only states what TM *is*, not what it can or can not do.

I say you can not come up with even an incomplete side-by-side listing of which method of Maths can do what.
 
Little 10 Toes said:
So only by using your terms/definitions (which constantly change and/or cannot be defined clearly), and buy using your plan (which has no improvements over current math) can you show something (which only you claim is important).
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It is clear that the realm of collections is naturally changeable, because no collection has the power of the continuum, which is not changeable w.r.t to the collections.
 
doronshadmi said:
It is clear that the realm of collections is naturally changeable, because no collection has the power of the continuum, which is not changeable w.r.t to the collections.
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Faulty premise. I define a collection and find elements that fit. What is "naturally changeable" about that?

By the way, my collection has a 18/00 strength, and that is before I count my +3 enchanted ring of hill giant strength.
 
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