Deeper than primes

doronshadmi · Oct 3, 2011

epix said:
Yes, your post is a collection of distinct objects called "words," but I don't understand how the set Post can be closed under collection of those words. The terminology "closed under" applies to the operations that the members of a set are subjected to. For example, R is closed strictly under addition and multiplication. You should explain what kind of operation the "collection of distinct object" is, otherwise you could be charged with forceful sodomy performed on juveniles. (The set theory is a relatively young field of mathematics.)

"Closed under" holds for any subject that is researched by using partial skills.

By using only verbal_symbolic skills in order to get the Mathematical science, one is actually closed under the limitations of partial abilities of one's skills.

Set theory in its classical form, is the result of using only verbal_symbolic skills.

By being closed under this limitation one actually can't understand the implications of non-homeomorphism among different mathematical/physical spaces.

As a result one can't comprehend Non-locality and Locality, Actual and potential infinity, the power of the continuum of a given "host" space w.r.t collections of "hosted" spaces on it, Cross-contexts and Context-dependent reasoning, and many more interesting facts that are available if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.

Please look at the following article http://arxiv.org/PS_cache/physics/pdf/0605/0605061v152.pdf which uses visual_spatial skills by translating them into verbal_symbolic skills.

By doing that verbal_symbolic AND visual_spatial skills still do not fulfill the ability to be used as a one comprehensive framework.

But by using verbal_symbolic AND visual_spatial skills, such that (for example) __ is 1-dim space and . is 0-dim space, it is obvious that . is the smallest possible space and no __ space can be . (and vise versa).

As a result __ is no more than smaller space w.r.t to . smallest space, such that given two smallest spaces .. there is always __ between them, which is no more then smaller space w.r.t them.

Furthermore, __ is located AND not located w.r.t each one of the two given smallest spaces .. exactly because it is no more than smaller space w.r.t to them.

On the contrary, a given . space is located XOR not located w.r.t to any given space that is not itself.

So by using verbal_symbolic AND visual_spatial skills one understands Non-locality and Locality.

epix · Oct 3, 2011

doronshadmi said:
"Closed under" holds for any subject that is researched by using partial skills.

By using only verbal_symbolic skills in order to get the Mathematical science, one is actually closed under the limitations of partial abilities of one's skills.

Set theory in its classical form, is the result of using only verbal_symbolic skills.

By being closed under this limitation one actually can't understand the implications of non-homeomorphism among different mathematical/physical spaces.

You seem to excel on the theme of the set closures, which is peculiar in the view of my statement

For example, R is closed strictly under addition and multiplication.

which you left floating on the surface of reason without raising any objection. Isn't it true that the example applies to N rather than to R?

Theories are usually rendered formally in the symbolic language, but they are not created that way. Some honest folks like Albert Einstein provided enough clue to what enters the mind. Actually Cantor believed that it was God who disclosed to him the "simple and beautiful" proofs. Andrew Wiles of the Last Fermat Theorem fame pretty much described what happened when he hit the dead end. God helps those who help themselves. In other words, you need to try and show willingness before tricks kick in. But there are plenty of ignorant pretenders who lie about the abilities of the human mind -- the mediocre of the flock who are not humble enough . . .

Is there something like the "second brain"?
http://www.lib.uni-bonn.de/PhiMSAMP/GAP6/Talks/Devlin.pdf

You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them. You can keep lying to yourself and continue your gobbledygook. That's not gibberish; the word actually stands for something:

Language that is meaningless or is made unintelligible by excessive use of abstruse technical terms; nonsense.

The visual representation of the set theory is unreliable:

T = {a, o, b}

(frui)T = {a, o, b}

T = {a, o, b}

jsfisher · Oct 3, 2011

doronshadmi said:
In my opinion, any definition is unsatisfied if it is not based on visual_spatial AND verbal_symbolic skills.

Talk about self-serving rubbish.... Since Doron has neither skill, his opinion is baseless.

Ideas can be expressed in words, and ideas can be expressed in images. Often times, words supplemented with images is a very effective presentation. Unfortunately for Doron, he has proven himself incapable of meaningful verbal or visual communication. Instead, he provides two seemingly uncorrelated versions of gibberish then blames everyone else for their lack of comprehension.

Rubbish.

doronshadmi · Oct 3, 2011

epix said:
You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them.

epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

zooterkin · Oct 3, 2011

doronshadmi said:
epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

I don't suppose you'd like to define either of those terms? Or would that require the use of interpretive dance?

epix · Oct 3, 2011

doronshadmi said:
epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

What makes you think that I don't understand the difference? Can you quote the post or a part of it that gave you the impression that I don't understand the difference?

Before that happens - if ever - I think you should get acquainted with an opinion of a mathematician who not only knows what he is doing but also how he is doing in it. I've already provided the link.

Of particular relevance to my thesis are the mathematicians’ descriptions of the way they arrived at the solutions to problems they had been working on. Time and again, the solution came at a quite unexpected moment, when the person was engaged in some other activity and was not consciously thinking about the problem. Moreover, in that inspirational moment the whole solution suddenly fell into place, as if the pieces of a huge jigsaw puzzle had been dropped onto the floor and miraculously landed as a complete picture. The mathematician “saw” the solution and instinctively knew it was correct.

No language is involved in this process. Indeed, with a problem for which the solution is fairly complex, it might take the mathematician weeks or even months to spell out (in linguistic form) the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result.

Here is a supporting word from Einstein and Hadamard respectively:

Words and language, whether written or spoken, do not seem to play any part in my thought processes. The psychological entities that serve as building blocks for my thought are certain signs or images, more or less clear, that I can reproduce and recombine at will.

I insist that words are totally absent from my mind when I really think . . . even after reading or hearing a question, every word disappears the very moment that I am beginning to think it over.

If you ponder the highlighted and imagine the very abbreviated explanation of topological spaces rendered in the formal language in Wikipedia, then it may take more than a month to set up the environment that leads toward understanding of the issue; and it takes a second to call anyone who peruses the text in order to learn the concept and claims that he now knows a liar.

Now you open your axioms with "C is a set" and then you put a restriction on one clause of the axiom, which prohibits "picking" one member no more than twice. Obviously, the confidence of the reader that you know what you are talking about is gone. Reminded of the problem, you change the definition from "C is a set" to "C stands for Collection" without bothering to specify the type of collection and the operation done on its members. Instead, you call upon those verbal_symbolic and spatial_visual skills to do the job. You offer repeatedly only one "spatial_visual" example, which is counter-intuitive, like any other of your visual supplements. Do you think I would bother to keep examining? I leave it to The Man or jsfisher, and then I read about it. If there is nothing to read about, then it's obvious that your "spatial_visual" argument is some kind of nonsense and my suspicion was correct.

Redo the circles, try again and again until a child understands it, if it's not a nonsense.

doronshadmi · Oct 4, 2011

epix said:
What makes you think that I don't understand the difference?

epix said:
Can you quote the post or a part of it that gave you the impression that I don't understand the difference?

Yes.

epix said:
You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them.

epix said:
Instead, you call upon those verbal_symbolic and spatial_visual skills to do the job. You offer repeatedly only one "spatial_visual" example, which is counter-intuitive, like any other of your visual supplements.

epix, it is counter-intuitive as long as you do not use verbal_symbolic AND spatial_visual skills as a one comprehensive framework.

By the way "the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result" is an example of using verbal_symbolic_only skills.

This time, please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7637828&postcount=16521 , before you are talking about counter-intuitive.

The Man · Oct 4, 2011

epix said:
That Ignore List is actually a subset, coz there are no duplicate nicknames in JREF. So if that subset comes under the influence of those two Doron's axioms, then the promised action taken by him can have an unexpected result, like he can even PM you.

If ‘PM’ means Purposely Misrepresent then that's about all he has been doing.

epix · Oct 4, 2011

doronshadmi said:
Yes.

epix, it is counter-intuitive as long as you do not use verbal_symbolic AND spatial_visual skills as a one comprehensive framework.

By the way "the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result" is an example of using verbal_symbolic_only skills.

This time, please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7637828&postcount=16521 , before you are talking about counter-intuitive.

Your verbal descriptions are almost always disconnected from your visual renditions. It only takes a few questions to confirm the suspicion that you are not at the helm of your own thoughts. You know it and that's why you ignore answering them or you perform an evasive maneuver. You are addicted to shuffling and connecting math terms that you read elsewhere and putting them stripped of any meaning on the billboard advertising Doronetics. And for the crimes committed against Plus and Minus, I therefore find you guilty as charged and hereby sentence you to counting to one hundred and backward with no possibility of skipping.

doronshadmi · Oct 6, 2011

epix said:
Your verbal descriptions are almost always disconnected from your visual renditions. It only takes a few questions to confirm the suspicion that you are not at the helm of your own thoughts. You know it and that's why you ignore answering them or you perform an evasive maneuver.

epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

This simple fact clearly shows that the power of continuum of 1-dimensional mathematical space is greater than the power of the collection of all 0-dimensional spaces on it.

Your inability to get what I have just wrote is beyond any suspicion, but you can't know that because your reasoning is closed under to power of the collection of all 0-dimensional mathematical spaces on (for example) a given 1-dimasional mathematical space (you wrongly define a given 1-dimensional mathematical space in terms of the 0-dimensional mathematical spaces on it).

Furthermore, you wrongly define the collection of all smallest objects ((known also as points or 0-dimensional mathematical spaces) on (for example) a given 1-dimensional mathematical space) as uncountable, exactly because you are not using also your visual_spatial skills, in order to really get this collection with respect to the power of the continuum of the "host" mathematical space (for example, the 1-dimensional mathematical space).

As a result all you get is the one-to-one correspondence between these smallest elements and their verbal_symbolic interpretations, known as the distinct members of R set.

By using only your verbal_symbolic skills you simply unable to get the 1-dimansiomal mathematical space between the members of R set, which is actually the "host" mathematical space of them that its power of continuum is inaccessible to R set (it is actually inaccessible to ...power(power(power(R)))... ad infinituum).

Because you are using only verbal_symbolic skills you can't actually understand the fact that the outer "{" and "}" symbols are exactly the inaccessibility of any given collection to the power of the continuum of a given "host" mathematical space (where the fact that "{""}" is the notation of the a given "host" mathematical space, is really understood only by using verbal_symbolic AND visual_spatial skills).

By using verbal_symbolic AND and visual_spatial skills it is immediately understood that no collection of "hosted" mathematical spaces has the power of the continuum of the "host" mathematical space.

Again, as long as your mathematical reasoning does not use verbal_symbolic AND and visual_spatial skills as a one comprehensive framework, you simply can't get this post.

jsfisher · Oct 6, 2011

doronshadmi said:
epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

The gibberish is strong in this one....

This simple fact clearly shows that the power of continuum of 1-dimensional mathematical space is greater than the power of the collection of all 0-dimensional spaces on it.

This would be true if the infinite behaved like the finite. It doesn't, and this isn't.

...<more nonsense>...

doronshadmi · Oct 6, 2011

Anyone that gets things only by verbal_symbolic skills, can't understand the lack of homeomorphism among different mathematical spaces.

Different mathematical spaces are distinct w.r.t each other, such that the greater mathematical spaces are the "host" mathematical spaces of the smaller (and therefore "hosted") mathematical spaces.

Being "hosted" means that the smaller (including the smallest) mathematical spaces are not the building-blocks of the "host" mathematical spaces, or in other words, the "host" mathematical spaces are not made of the "hosted" mathematical spaces.

The smallest mathematical space is 0-dimansional space, which is stronger than emptiness (where emptiness is that has no predecessor), and all the possible infinitely many mathematical spaces that are greater than 0-dimensional mathematical space, are smaller than fullness (where fullness is that has no successor).

Emptiness is the weakest limit of the mathematical science.

Fullness is the strongest limit of the mathematical science.

Collections are the intermediate mathematical universe, which is considered as intermediate if it is inaccessible to these limits.

Unity is absolute symmetry, such that Emptiness,Fullness and the intermediate mathematical universe, are indistinguishable.

jsfisher · Oct 7, 2011

doronshadmi said:
...<self-serving gibberish>...

So, when Doron said he was ignoring several of us, he wasn't being completely honest. I'm shocked, I tell you. Shocked!

epix · Oct 7, 2011

doronshadmi said:
epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

In my practical applications, I treat points as a dimensionless reference and so your superlatives, like "smallest," are meaningless in that respect. Show me an example, a real computational problem, where in order to solve it, I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

I can only guess, but it seems to me that you may not be aware of a certain difference. Check out this hardware:
http://www.maniacworld.com/flash-chess.jpg

The stones move around the board according to a set of rules -- you can liken them to axioms. The rules are invariant.

Now check out this hardware:
http://static.howstuffworks.com/gif/poker2.jpg

There are 52 cards in the deck, and, unlike in chess, there are many sets of rules, each set defining a different card game: there are rules (axioms) according to which poker is played, there are rules (axioms) according to which blackjack is played, and so on. But you think that there is only one true card game -- some doron canasta -- and you are trying to invent the rules for it thinking that all other card games are biased to a lesser or greater extent. Every card player knows what "flush" means, but you love to rename the established and come up with your own terms, maybe like "local toilet," and relentlessly try to teach your invention to others -- a card game invention where king of spades is less than king of hearts, but queen of spades beats queen of hearts including all sevens AND eights AND the aces, but not two of diamonds. Your rules (axioms) are too weird and outright illogical for any game apart from howhigh solitaire.

doronshadmi · Oct 7, 2011

epix said:
In my practical applications, I treat points as a dimensionless reference and so your superlatives, like "smallest," are meaningless in that respect.

0-dimesional mathematical space is not the same as the lack of mathematical dimensional space.

Actually because you are using only verbal_symbolic skills in order to understand what I wrote above, you can't comprehend the difference between 0-dimesional mathematical space and the lack of lack of mathematical dimensional space (called by you "dimensionless").

Once again it is shown that if one does not use verbal_symbolic AND visual_spatial skills as a one comprehensive framework, one actually fails to comprehend the discussed fine subject.

epix said:
Show me an example, a real computational problem, where in order to solve it, I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

Once again, 0-dimesional mathematical space is not the same as the lack of dimension, exactly as the cardinality of the empty set (=0) is not the same as Emptiness).

0 is understood by verbal_symbolic skills and Emptiness is understood by visual_spatial skills, and the difference between (for example) 0 cardinality and (for example) Emptiness, is understood only if one uses verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

epix, you still do not do anything in order to get the discussed fine subject by using verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

If you actually use verbal_symbolic AND visual_spatial skills as a one comprehensive framework, then (and only then) you can understand the following:

doronshadmi said:
The smallest mathematical space is 0-dimansional space, which is stronger than emptiness (where emptiness is that has no predecessor), and all the possible infinitely many mathematical spaces that are greater than 0-dimensional mathematical space, are smaller than fullness (where fullness is that has no successor).

Emptiness is the weakest limit of the mathematical science.

Fullness is the strongest limit of the mathematical science.

Collections are the intermediate mathematical universe, which is considered as intermediate if it is inaccessible to these limits.

Unity is absolute symmetry, such that Emptiness,Fullness and the intermediate mathematical universe, are indistinguishable.

epix said:
I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

By your own words you ascribed "zero" as the dimensional mathematical space of a point, where no line segment has "zero" mathematical dimensional space (it approaches AND not reaches "zero" mathematical dimensional space (this time please actually do your best in order to get http://www.internationalskeptics.com/forums/showpost.php?p=7540470&postcount=16339)).

epix said:
But you think that there is only one true card game -- some doron canasta --

Wrong, there are infinitely many context-dependent games (each game has its own rules) AND cross-contexts principle of being a game.

In other words, in this case you have failed to get "game" as the "host" cross-context mathematical space, and the infinitely many context-dependent games as the "hosted" mathematical spaces.

doronshadmi · Oct 7, 2011

Enjoy : http://www.youtube.com/watch?v=YOQb_mtkEEE&feature=related

doronshadmi · Oct 8, 2011

By using the fact that we are dealing with collections of distinct objects, let us re-search such collections by understanding notations according to verbal_symbolic AND visual_spatial skills.

The cardinality of Fullness is |{}| = ∞, where Fullness (that has no successor) is notated by the outer "{" and "}".

The cardinality of Emptiness is {||} = 0, where Emptiness (that has no predecessor) has no notation.

By understanding the difference between |{}| and {||}, we are able to deal with cardinality which is > {||} AND < |{}|, for example, such that {|...|} < |{...}|, where "..." is a general notation of members.

{|{}|} = 1

|{{}}| = ∞ because Fullness has no successor (its cardinality is inaccessible to all that have cardinality with successors (whether the amount of successors is finite or not).

Generally, all that have cardinality with successors, such cardinality is notated (for example) as {||}, {|a|}, {|a,b|}, {|a,b,c|} , ... etc. in the case of finite cardinality, or notated (for example) as {|,a,b,c,...|} in the case of infinite cardinality.

Russell's paradox is naturally solved as follows:

|{,a,b,c,...}| = ∞

{|,a,b,c,...|} < ∞

{|,{,a,b,c,...},a,b,c,...|} < ∞ = |{,{,a,b,c,...},a,b,c,...}|

Generally , the cardinality of all given collections with distinct objects < cardinality ∞.

So no collection of distinct objects can be its own member, because being a member of collection of distinct members, does not change the fact that the cardinality of all members of a given collection of distinct objects < ∞.

By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) of a given collection (which is not less than "host" mathematical space) is equivalent to the given collection.

zooterkin · Oct 8, 2011

doronshadmi said:
Generally , the cardinality of all given collections with distinct objects < cardinality ∞.

Are you saying that the cardinality of the set of positive integers (which are distinct objects) is not ∞?

doronshadmi · Oct 8, 2011

zooterkin said:
Are you saying that the cardinality of the set of positive integers (which are distinct objects) is not ∞?

∞ < ∞, where ∞ is the cardinality of Fullness (that has no successor) and ∞ is the cardinality of infinite collections on it (which are incomplete w.r.t to it, since no matter how infinitely many successors (immediate or non-immediate) they have, the cardinality of Fullness (∞) is inaccessible to them).

Fullness (that has no successor) is the "host" mathematical space, which is naturally beyond the power of all infinite collections (they have successors) which are "hosted" mathematical spaces on it.

By understanding this simple fact, it is realized that no collection of "hosted" mathematical spaces have the power of the "host" space, or in other words, the cardinality of the "hosted" mathematical spaces (and members are such spaces) < cardinality of the "host" space.

Fullness is shown, for example, by the non-locality of 1-dimensional "host" mathematical space w.r.t all infinite "hosted" mathematical spaces (whether they are infinite collections of points or line segments on it), which are local w.r.t the 1-dimensional "host" mathematical space.

As long as you do not get the mathematical science as Cross-contexts (Non-locality, or "host" mathematical space) AND Context-dependent (Locality, or "hosted" mathematical spaces) as a one comprehensive framework, you can't comprehend this post.

Once again, Cardinality is between the cardinality of Emptiness (that has no predecessor, which is notated as {||}) and the cardinality of Fullness (that has no successor, which is notated, at least, as |{}|).

Some claims: "1-dimensional mathematical space does not have the cardinality of fullness since it has, for example, 2-dimensional mathematical space as its successor, and so on ... ad infinituum".

Well, the important fact is the "host"\"hosted" principle between mathematical spaces, which is defined exactly because of the inaccessibility of the cardinality of Fullness to all mathematical spaces, which have successors (immediate or not).

Mathematical spaces are considered as collections w.r.t any given "host" mathematical space, which is derived from the "host"\"hosted" principle between mathematical spaces.

The existence of fundamental principle among infinitely many levels of a given non-trivial system, is actually one of the beauties of Cross-contexts AND Context-dependent framework.

Unity is the symmetry that prevents the distinction between Emptiness, Fullness, and everything between them.

doronshadmi · Oct 8, 2011

Let's correct the last paragraph of http://www.internationalskeptics.com/forums/showpost.php?p=7653835&postcount=16537.

Instead of

doronshadmi said:
By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) of a given collection (which is not less than "host" mathematical space) is equivalent to the given collection.

It has to be:

By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) is equivalent to the "host" mathematical space.

The Man · Oct 9, 2011

doronshadmi said:
By using the fact that we are dealing with collections of distinct objects, let us re-search such collections by understanding notations according to verbal_symbolic AND visual_spatial skills.

Just making up crap still does not constitute research.

doronshadmi said:
The cardinality of Fullness is |{}| = ∞, where Fullness (that has no successor) is notated by the outer "{" and "}".

The "{" and "}" are inside not outside the only other symbols in your purported notation, so much for your “visual_spatial skills”.

doronshadmi said:
The cardinality of Emptiness is {||} = 0, where Emptiness (that has no predecessor) has no notation.

And once again you give notations to what you claim “has no notation”, so much for your “verbal_symbolic skills”.

Well that’s two out of three down, you also claimed you would be “using the fact that we are dealing with collections of distinct objects”, let’s see how that pans out.

doronshadmi said:
By understanding the difference between |{}| and {||}, we are able to deal with cardinality which is > {||} AND < |{}|, for example, such that {|...|} < |{...}|, where "..." is a general notation of members.

{|{}|} = 1

Everyone here, but you, has no problem dealing with cardinality without any of your nonsense.

doronshadmi said:
|{{}}| = ∞ because Fullness has no successor (its cardinality is inaccessible to all that have cardinality with successors (whether the amount of successors is finite or not).

Well that just makes your “Fullness” useless, congratulations.

doronshadmi said:
Generally, all that have cardinality with successors, such cardinality is notated (for example) as {||}, {|a|}, {|a,b|}, {|a,b,c|} , ... etc. in the case of finite cardinality, or notated (for example) as {|,a,b,c,...|} in the case of infinite cardinality.

No it isn’t see again Cardinality.

doronshadmi said:
Russell's paradox is naturally solved as follows:

|{,a,b,c,...}| = ∞

{|,a,b,c,...|} < ∞

{|,{,a,b,c,...},a,b,c,...|} < ∞ = |{,{,a,b,c,...},a,b,c,...}|

Nope, you just mis-mashing symbols together doesn’t solve anything other than simply your pretence that you have any “verbal_symbolic AND visual_spatial skills” whatsoever.

doronshadmi said:
Generally , the cardinality of all given collections with distinct objects < cardinality ∞.

“Generally”? So not always? When does the “cardinality of all given collections with distinct objects change such that “< cardinality ∞” does not apply?

doronshadmi said:
So no collection of distinct objects can be its own member, because being a member of collection of distinct members, does not change the fact that the cardinality of all members of a given collection of distinct objects < ∞.

Since when is changing “the fact that the cardinality of all members of a given collection of distinct objects < ∞” a requirement for a collection of distinct objects being its own member?

doronshadmi said:
By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) of a given collection (which is not less than "host" mathematical space) is equivalent to the given collection.

If the collection were a member of itself then the collection would be equal to at least one member of the collection. All you have done is to simply assert that “no collection of distinct objects can be its own member” because it does not change some irrelevant nonsense about your “∞” that you assert above “is inaccessible to all that have cardinality with successors”. Again congratulations not only have you failed to use “the fact that we are dealing with collections of distinct objects” as you claimed above you tried using just your claim that your “inaccessible” “∞ remains, well, “inaccessible” simply by your own edict.

That’s three for three.

Your failure is now complete.

jsfisher · Oct 9, 2011

Excellent. Doron wasn't sufficiently confused and confusing with his old notation, so he's now moved on to a new notation.

epix · Oct 9, 2011

doronshadmi said:
By understanding the difference between |{}| and {||}, we are able . . .

. . . to define the host space.

doronshadmi · Oct 9, 2011

It has to be stressed that there is difference between "defined by" and "made of".

For example, 1-dimensional space is defined as "host" mathematical space w.r.t to 0-demensional spaces or segments on it, where the 0-demensional spaces or segments on it are defined as "hosted" mathematical spaces w.r.t it.

"host"\"hosted" mathematical spaces depends on each other in terms "defined by".

"host"\"hosted" mathematical spaces do no depend on each other in terms "made of", for example (without loss of generality): 1-dimensional mathematical space is not made of 0-dimensonal mathematical spaces or segments on it.

The difference between "defined by" and "made of" is easily understood if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.

epix · Oct 9, 2011

The Man said:
And once again you give notations to what you claim “has no notation”, so much for your “verbal_symbolic skills”.

Doron uses some standard terminology and symbols, but shuffles the latter around at will. The size of a set is usually denoted the same way as the absolute value - the argument appears between two parallel vertical lines. Perhaps because of taking "Emptiness" literally, it never appears as the argument inside | | as he demonstrates here:

The cardinality of Emptiness is {||} = 0, where Emptiness (that has no predecessor) has no notation.

You expect the cardinality of Emptiness is |E| = 0, but instead of finding argument E inside | |, the term "Emptiness" gets symbolized by the braces { } and, as the argument, gets placed outside

| |. There is also a big chance that Doron invented special cardinality symbol for the size of Emptiness that reads {||} and means that set Emptiness has no membership whatsoever. (Emptiness doesn't have to be necessarily a set; it can be some collection whose meaning and function can be understood only when some x_y skills kick in.)

I can't wait when the moment filled with the spirit of fecundity arrives and we'll see some arithmetic performed on delimiters.

doronshadmi · Oct 9, 2011

epix said:
Emptiness doesn't have to be necessarily a set; it can be some collection ...

No, it can't be some collection, because Emptiness is the predecessor of the concept of Collection, but not vice versa.

By using the same reasoning, Fulness (which is the opposite of Emptiness) is the successor of the concept of Collection, but not vise versa.

In terms of Cardinality {||} = 0 (where 0 in the measurement of Emptiness and not Emptiness itself).

In terms of Cardinality |{}| = ∞ (where ∞ is the measurement of Fullness and not Fullness itself).

The Cardinality of Collections > 0 AND < ∞, such that 0 < n < ∞ < ∞.

The Man · Oct 9, 2011

epix said:
Doron uses some standard terminology and symbols, but shuffles the latter around at will. The size of a set is usually denoted the same way as the absolute value - the argument appears between two parallel vertical lines. Perhaps because of taking "Emptiness" literally, it never appears as the argument inside | | as he demonstrates here:

You expect the cardinality of Emptiness is |E| = 0, but instead of finding argument E inside | |, the term "Emptiness" gets symbolized by the braces { } and, as the argument, gets placed outside | |. There is also a big chance that Doron invented special cardinality symbol for the size of Emptiness that reads {||} and means that set Emptiness has no membership whatsoever. (Emptiness doesn't have to be necessarily a set; it can be some collection whose meaning and function can be understood only when some x_y skills kick in.)

I can't wait when the moment filled with the spirit of fecundity arrives and we'll see some arithmetic performed on delimiters.

Actually it is just a reversal (the inside symbols become the outside) of his “notation” for “fullness” “|{ }|” (which ironically would normally be taken as the cardinality of the empty set). Doron is attempting to internalize his “cardinality” by putting the “|” symbols inside, indicating cardinality inside the collection (symbolized by the brackets). In that lay the failure epix, not only in the word “Emptiness” which is a notation for his concept of emptiness but also the blank space between “| |” inside the brackets where he literally and symbolically attempts to notate that concept and indicate his “cardinality” of it. Even in spite of his claims that it “has no notation” and that everyone should just get the concept through “direct perception”, he still evidently knows that he must notate it somehow to communicate that concept and what he wants to claim about it. Thus the result is that his attempts at both verbal and visual communication are just half assed and self contradictory because he really doesn’t want to believe he needs them in spite his apparent understanding that he does.

The Man · Oct 9, 2011

doronshadmi said:
No, it can't be some collection, because Emptiness is the predecessor of the concept of Collection, but not vice versa.

By using the same reasoning, Fulness (which is the opposite of Emptiness) is the successor of the concept of Collection, but not vise versa.

In terms of Cardinality {||} = 0 (where 0 in the measurement of Emptiness and not Emptiness itself).

In terms of Cardinality |{}| = ∞ (where ∞ is the measurement of Fullness and not Fullness itself).

The Cardinality of Collections > 0 AND < ∞, such that 0 < n < ∞ < ∞.

And there you have it epix, the symbols themselves are meaningless. It is only there configuration that is intended to carry meaning by Doron. In this case it is the simple reversal of ordering (the inside symbols become the outside) that is intend to convey his preferred ordering. So Doron has now specifically asserted that his “Emptiness” and “Fullness” are both beyond “the concept of Collection” (though evidently not beyond the concept of ordering) and, as we all already understood, thus irrelevant to that concept, though it may take another 20 some odd years for it to sink in with him.

The Man · Oct 10, 2011

doronshadmi said:
It has to be stressed that there is difference between "defined by" and "made of".

For example, 1-dimensional space is defined as "host" mathematical space w.r.t to 0-demensional spaces or segments on it, where the 0-demensional spaces or segments on it are defined as "hosted" mathematical spaces w.r.t it.

"host"\"hosted" mathematical spaces depends on each other in terms "defined by".

"host"\"hosted" mathematical spaces do no depend on each other in terms "made of", for example (without loss of generality): 1-dimensional mathematical space is not made of 0-dimensonal mathematical spaces or segments on it.

The difference between "defined by" and "made of" is easily understood if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.

It has to be stressed and apparently repeated that being defined as, as in a line and/or line segment being define as a collection of points and/or a line being defined as a collection of line segments (themselves being define by points and as a collection of points), means exactly what it says. It looks like your conflation de jour is to simply replace your “non-local” with “host” and your “local” with “hosted” while still leaving them all, “defined as”, "defined by" and certainly "made of", well, nothing.

epix · Oct 10, 2011

The Man said:
Actually it is just a reversal (the inside symbols become the outside) of his “notation” for “fullness” “|{ }|” (which ironically would normally be taken as the cardinality of the empty set).

That's right - under the normal circumstances, which is obviously not the case.

I think that Doron got inspired by the fact that the space between | and | is not empty - it's occupied by {} - and therefore it's full. But in case of {||}, the space between both vertical lines is empty. Under the normal circumstances, {||} indicates a set with one member and that's '||' and that means the set is not empty, but since things are the other way - they are far from being normal - Doron links {||} with his peculiar concept of Emptiness.

epix · Oct 10, 2011

doronshadmi said:
In terms of Cardinality {||} = 0 (where 0 in the measurement of Emptiness and not Emptiness itself).

In terms of Cardinality |{}| = ∞ (where ∞ is the measurement of Fullness and not Fullness itself).

The Cardinality of Collections > 0 AND < ∞, such that 0 < n < ∞ < ∞.

But that greatly reduces the modus operandi of your space - it becomes very restrictive. In other words, your space wouldn't be able to contribute to the solution of

{x}

for x, which is the fundamental unsolved problem of contemporary mathematics.

doronshadmi · Oct 10, 2011

Continuation - Deeper than primes

epix said:
I think that Doron got inspired by the fact that the space between | and | is not empty - it's occupied by {} - and therefore it's full.

You are still missing it.

"|" and "|" are the notations of cardinality.

{||} = 0, where 0 is the cardinality of Emptiness, where Emptiness (that has no predecessor) is not the same as 0.

|{}| = ∞, where ∞ is the cardinality of Fullness, where Fullness (that has no successor) is not the same as ∞.

You still do not get the meaning of the outer "{" and "}" w.r.t what is found (or not) between them.

As about Emptiness, please pay attention that no notation (including space bar) is used between || (|| + space bar is | |, so there is no notation between "|" and "|" (which notated only by || for the cardinality of Emptiness)).

epix said:
In other words, your space wouldn't be able to contribute to the solution of

{x}

for x, which is the fundamental unsolved problem of contemporary mathematics.

Wrong, you still do not get the inaccessibility of cardinality {|x|} to cardinality |{x}|, such that cardinality {|x|} measures the naturally open realm, exactly because it is inaccessible to cardinality |{x}|.

doronshadmi · Oct 10, 2011

About Fullness, it is defined as the opposite as Emptiness, but it is not made of Emptiness or any collection of objects.

About Emptiness, it is defined as the opposite as Fullness, but it is not made of Fullness or any collection of objects.

Also Cardinality can be ordered (as shown in http://www.internationalskeptics.com/forums/showpost.php?p=7656719&postcount=16546) but the order of objects under a given cardinality > 1 AND < ∞ has no significance.

doronshadmi · Oct 10, 2011

Some typo corrections of http://www.internationalskeptics.com/forums/showpost.php?p=7658997&postcount=16553.

Instead of "opposite as Emptiness" is has to be "opposite of Emptiness".

Instead of "opposite as Fullness" is has to be "opposite of Fullness".

So, the right one is

doronshadmi said:
About Fullness, it is defined as the opposite of Emptiness, but it is not made of Emptiness or any collection of objects.

About Emptiness, it is defined as the opposite of Fullness, but it is not made of Fullness or any collection of objects.

Also Cardinality can be ordered (as shown in http://www.internationalskeptics.com/forums/showpost.php?p=7656719&postcount=16546) but the order of objects under a given cardinality > 1 AND < ∞ has no significance.

jsfisher · Oct 10, 2011

doronshadmi said:
About Fullness, it is defined as the opposite as Emptiness, but it is not made of Emptiness or any collection of objects.

About Emptiness, it is defined as the opposite as Fullness, but it is not made of Fullness or any collection of objects.

Doron loves circles.

epix · Oct 10, 2011

Originally Posted by epix
In other words, your space wouldn't be able to contribute to the solution of

{x}

for x, which is the fundamental unsolved problem of contemporary mathematics.

doronshadmi said:
Wrong, you still do not get the inaccessibility of cardinality {|x|} to cardinality |{x}|, such that cardinality {|x|} measures the naturally open realm, exactly because it is inaccessible to cardinality |{x}|.

Quit fantasizing. The reason for the inaccesibility lies elsewhere, and I will explain it. Btw, your set doesn't live in a topological space and it is not closed and at the same time opened,
http://en.wikipedia.org/wiki/Clopen_set
so it cannot fully address the issue that relates to the solution of {x}.

Unlike you, I can provide an example of what I'm saying. The interim solution is bivariate

1. {x} = 32
2. {x} = 28

but it's hard to arrive at the unique solution.
Let x be enclosed in braces {}. It follows that {x} is a set. The answer to the question of what kind of set is given by the closure, which are the braces, and so the set is definable.

We know from the definition of the set that the host space is opened and closed w.r.t. the variable x. That's because the cardinality of the set of teeth is 32, but the wisdom teeth are sometimes removed from the host space, and so the cardinality is reduced to 28. There is no way of determining the unique value of x unless the host space is only and only opened. But it takes Clifford algebra
http://en.wikipedia.org/wiki/Clifford_algebra
and a special set up
http://tucsondental.org/wp-content/uploads/2010/05/Chair.jpg

to accomplish the transformation that leads toward :jaw-dropp

.

The Man · Oct 11, 2011

jsfisher said:
So, when Doron said he was ignoring several of us, he wasn't being completely honest. I'm shocked, I tell you. Shocked!

Evidently, but given his propensity for self contradiction and only self deception the only way he can ignore us is to read what we post and respond to it while pretending (only to himself) that he is not.

doronshadmi said:
Also Cardinality can be ordered (as shown in http://www.internationalskeptics.com/forums/showpost.php?p=7656719&postcount=16546) but the order of objects under a given cardinality > 1 AND < ∞ has no significance.

“can be ordered”? You just asserted above the particular ordering you insist upon.

doronshadmi said:
No, it can't be some collection, because Emptiness is the predecessor of the concept of Collection, but not vice versa.

By using the same reasoning, Fulness (which is the opposite of Emptiness) is the successor of the concept of Collection, but not vise versa.

Predecessor and successor are both assertions of ordering (as has been pointed out to you multiple times before).

doronshadmi said:
…the order of objects under a given cardinality > 1 AND < ∞ has no significance.

Really? Well let’s try…

We have (in your prefered ordering)…

“Emptiness is the predecessor of the concept of Collection”

Then

“the concept of Collection”

And then

“Fulness (which is the opposite of Emptiness) is the successor of the concept of Collection”

Well that’s just three of your ‘concepts’ “Emptiness”, “Collection” and “Fulness”

As 3 is “> 1 AND < ∞” your preferred ordering of your purported concepts has, by your own assertion, “no significance”.

See that wasn’t so hard to figure out and only took you pretending to ignore what was posted as opposed the 20 some odd years you spent ignoring just about everything but your own ‘concepts’.

This pretend ignorance of yours seems to be working better for you and everyone else as opposed to just the actual blatant ignorance you normally steep yourself in.

doronshadmi · Oct 11, 2011

epix said:
Originally Posted by epix
In other words, your space wouldn't be able to contribute to the solution of

{x}

for x, which is the fundamental unsolved problem of contemporary mathematics.

Quit fantasizing. The reason for the inaccesibility lies elsewhere, and I will explain it. Btw, your set doesn't live in a topological space and it is not closed and at the same time opened,
http://en.wikipedia.org/wiki/Clopen_set
so it cannot fully address the issue that relates to the solution of {x}.

Unlike you, I can provide an example of what I'm saying. The interim solution is bivariate

1. {x} = 32
2. {x} = 28

but it's hard to arrive at the unique solution.
Let x be enclosed in braces {}. It follows that {x} is a set. The answer to the question of what kind of set is given by the closure, which are the braces, and so the set is definable.

We know from the definition of the set that the host space is opened and closed w.r.t. the variable x. That's because the cardinality of the set of teeth is 32, but the wisdom teeth are sometimes removed from the host space, and so the cardinality is reduced to 28. There is no way of determining the unique value of x unless the host space is only and only opened. But it takes Clifford algebra
http://en.wikipedia.org/wiki/Clifford_algebra
and a special set up
http://tucsondental.org/wp-content/uploads/2010/05/Chair.jpg

to accomplish the transformation that leads toward .

The outer "{" "}" (Fullness) is not a member of any collection, and so is Emptiness (which has no notation).

"x" of {x} is a placeholder of collections, which their cardinality (notated as {|x|}) is > 0 AND < ∞, simply because the outer "{" "}" (Fullness) is not a member of any collection, and so is Emptiness (which has no notation at all (including space bar)).

So the cardinality of a given collection (notated as {|x|}) is greater than the cardinality of Emptiness ({||} = 0, where 0 is not Emptiness itself) and smaller than the cardinality of Fullness (|{}| = |{x}| = ∞, where ∞ is not Fullness itself).

Furthermore, there is a difference between the names of concepts, which can be members of a given collection, and the concepts themselves, for example: the names Emptiness or Fullness are two distinct members of a given collection, but the concepts Emptiness or Fullness themselves are not members of any given collection.

Your example uses notations that are meaningless by standard notation and also by my non-standard notation.

Let's give them some meaning:

x is a placeholder for collection of members.

My non-standard notation (and notion) {|x|} is equivalent to standard notation (and notion) |{x}|.

My non-standard notation (and notion) {||} is equivalent to standard notation (and notion) |{}|.

My non-standard notation (and notion) |{x}| = ∞ is not equivalent to standard notation (and notion) |{x}|.

My non-standard notation (and notion) |{}| = ∞ is not equivalent to standard notation (and notion) |{}| = 0.

Also the order of the members of a given collection that its cardinality > 1 AND < ∞ has no significance.

Persons that put any given concept as a member of some collection, simply can't deal with concepts that are not members of collections (they can't distinguish between the name of a given concept, which is defiantly some member of a given collection, and the concept itself, where the concept itself is not necessarily a member of any given collection, as can be seen in the case of Emptiness or Fullness).

doronshadmi · Oct 11, 2011

Unity awareness

Awareness' development is first of all self awareness of finer levels of one's thinking process (no matter what meaning is given to thoughts) until one is aware of the finest state of awareness, which is naturally free of any thinking process (it is not a thought or collection of thoughts).

The development of one's awareness is the self ability to be aware of the finest level without losing it during the thinking process, such that both calmness and activity are present in one's mind without prevent each other.

By developing such state of mind, one is at the optimal expressions' abilities , which is naturally free of contradiction w.r.t other expressions, exactly because one's mind expresses itself right from the source of all possible expressions.

Organic Mathematics is first of all a systematic method that uses mathematical insights in order to open one's mind to the Unity of simplicity (calmness) and activity (complex expressions).

Here is some analogy using 1-dimensional space as the Unity of both straight-line (calmness) and curved-lines (complex expressions), as shown by the following diagram:

[qimg]http://farm4.static.flickr.com/3296/5721561558_c5b78c3152_b.jpg[/qimg]

By gently meditate on the following diagram one is opened to the non-subjective level of awareness (illustrated by the straight line), at least at the level of the analogy (which is not the actual non-subjective state of mind).

By this analogy the 1 dimensional space is the Unity of any possible form, such that being straight or not is not known in terms of dichotomy.

Please look also at http://www.internationalskeptics.com/forums/showpost.php?p=7654162&postcount=16539 which is ended by this line:

doronshadmi said:
Unity is the symmetry that prevents the distinction between Emptiness, Fullness, and everything between them.

This symmetry actually prevents the distinction between Emptiness, Fullness, and everything between them, such that they are directly known as "organs of a one realm".

Persons that are not able to be aware of their non-subjective level, can't get the awareness of Unity, which is not a thought about Unity (or, by analogy, the name of a given concept is not the concept itself).

doronshadmi · Oct 11, 2011

Let's correct the last paragraph of http://www.internationalskeptics.com/forums/showpost.php?p=7662467&postcount=16558.

Instead of

doronshadmi said:
Persons that put any given concept as a member of some collection, simply can't deal with concepts that are not members of collections (they can't distinguish between the name of a given concept, which is defiantly some member of a given collection, and the concept itself, where the concept itself is not necessarily a member of any given collection, as can be seen in the case of Emptiness or Fullness).

it has to be

Persons that put any given concept as a member of some collection, simply can't deal with concepts that are not members of collections (they can't distinguish between the name of a given concept, which is definitely some member of a given collection, and the concept itself, where the concept itself is not necessarily a member of any given collection, as can be seen in the case of Emptiness or Fullness).

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