Deeper than primes

[The Man]

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.

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”.

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.

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.

|{{}}| = ∞ 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.

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.

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.

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?

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?

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]

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

 

[epix]

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

. . . to define the host space.

 

[doronshadmi]

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]

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]

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]

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]

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]

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]

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]

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]

Continuation - Deeper than primes

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)).

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]

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]

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

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]

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]

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.

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 .

 

[The Man]

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.

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.

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).

…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]

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]

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:

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]

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

Instead of

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).