Deeper than primes

[doronshadmi]

I guess you now agree with what I had always said on the other thread that your assertions and ascriptions (local and non-local) are just a matter of perspective.

In the case of an object like line, I agree with you.

The alternatives are yours,

Yes indeed. Because there are alternatives, where no alternative is exclusive.

But someone like you that have no alternatives, has no choice but to use the exclusive case of serial observation.

Exclusive means that no other observation is allowed except the exclusive one (which is your case is the serial-only case, that has no alternatives).

 

[doronshadmi]

0 nxor 0 --> 0
0 nxor 1 --> 1
1 nxor 0 --> 1
1 nxor 1 --> 0

This is not NXOR. This is XOR.

You still don't understand that term, do you?

You still do not understand the generalization, do you?

 

[The Man]

In the case of an object like line, I agree with you.

Ok, so how about considering the line as a whole or as a combination of sub elements as a matter of perspective as well?

Yes indeed. Because there are alternatives, no alternative is exclusive.

I think you still need a better understanding of the term “exclusive” all alternatives that are not inclusive are by default exclusive or exclude the other alternatives not selected or not included.

But someone like you that have no alternatives, has no choice but to use the exclusive case of serial observation.

Again you are the one claiming “no choice” and “no alternatives” because as you assert.

In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.

Exclusive means that no other observation is allowed except the exclusive one (which is your case is the serial-only case, that has no alternatives).

Well that is precisely what you have asserted above that no other observation of “___” “In this case” except your exclusive “parallel observation”. So I will ask again just what do you think you are observing exclusively in “parallel”?

 

[jsfisher]

This is not NXOR. This is XOR.

You are correct in this, of course. My mistake. Permit me to correct my typographic error and re-present my questions:

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

 

[Little 10 Toes]

I will answer your questions out of order:

This is not my definiton for at least two reasons:

1) Subset is not the same as proper subset.

2) You ignored the term "cannot be but |B| < |A|".

1)It's not my fault that you are not using non-standard terms. You have not defined "proper subset". I defined subset, and used it accordingly. Please give your definition of subset and proper subset. Please then explain the differences.

2) Yes I have. "Cannot be but" is the same as "then". Example: If you continue to use standard terms in non-standard ways, you cannot be but misunderstood by 99.9% of the posters. If you use too many words when few will do, you cannot but be looked upon as being unclear.

Definition 2: Set A is called finite if the cardinal of proper subset B of A cannot be but |B| < |A|.

Definition 2 says that A is finite if its proper subset cannot be but |B| < |A|

What is not clear here? I do not think that by definition 2 we can conclude that property not-X is non-finite.

What do you mean by property? We are only talking about if a set is either finite or non-finite based only on cardinality, not "not-X". In your quoted messages contained in this post, your definitions of #2 and #3 only talk about finite and non-finite.

Let us try this version of definition 3:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A can be (|B| < |A|) AND (|B| = |A|).

Using an example, how can 3 be equal and less than 4? Cardinality does not care about the members of a set, it just cares about how many, and then we compare those two values, using def #3, to see if set A is non-finite.

Little 10 Toes,

If we observe a non-local element, its value can be in more than a one relation w.r.t another element.

But this is not the case here.

Then why bring it up?

In this case I am trying to define the difference between finite and non-finite sets, where each member is local (can be distinguished from another member by using only one relation).

You have not defined "local". Defs #2 and Def #3 are only talking about cardinality, sets, and subsets. They don't mention members at all. Why are you bringing up members when you only care about defining finite and non-finite sets? One of your posts mention that want to define sets, but do not mention members. In fact, you posted this before I posted my message, remember?

(quoted message that does not show when I quote this message)
"Cannot be but ..." is an understatement of "must be ..." and I prefer to use understatements.
(another quoted message that does not show when I quote this message)
It will be come later.

At this stage I wish to clearly distinguish between finite and non-finite sets.

Please answer to http://www.internationalskeptics.com/forums/showpost.php?p=4236183&postcount=896 .

Let's continue with the original post:

Let us use the notion of proper subset in order to distinguish between finite and non-finite sets as follows:

Definition 3: If A is a set and B is some arbitrary proper subset of A, then if |B| cannot be but |B| < |A|, then A is finite.

If we can use definition 3 in order to conclude that anything that does not satisfy it, must be a non-finite set, then definition 3 is enough to distinguish between finite and non-finite sets.

What do you think?

Well, it woud be nice to use the notion, but since you have a history of springing new words, or using common words but with different standard definitions, I can't since you have not defined "proper subset". In addition, you did not dispute my example of set A being all positive whole even numbers, and set B being all positive whole even numbers evenly divisible by five. Most mathematicians would say both sets are infinite, but by using def #2, set A is finite.




I think you are overthinking things. Would you agree to the following definitions of the following terms:

• CardinalityWP: "In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3." Using the example set shown, I will use the notation |A| = 3 .
• SubsetWP: "In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide."
• Infinite: something that has no end or begining; something that cannot have a value attached to; unmeasurable/uncountable; unquantifiable. Example, the smallest/largest number; in geometry, a line. Synonym^WP: non-finite.
• Finite: something that does have an end; can have a value attached to; measurable/countable; practical; quantifiable. Example: the number of coins in my pocket, the number of grains of sand on a beach; in geometry, a line segment
• "Cannot be but": synonym of "then"

Do you agree to these definitions to the words?

If you only think about sets and subsets, and use "standard" mathematical "grammer", my definitions are the same as yours, just cleaner. Can you give me your definition of subset, proper subset, and the difference between the two without using examples until requested?

 

[doronshadmi]

So I will ask again just what do you think you are observing exclusively in “parallel”?

No.

I observe ___ from more than a one and only one point of view.

In the case of observation from x to y:

1) If x = . and y = ___ and the researched case is _._ , then x = y from x point of view.

2) If x = __ and y = . and the researched case is _._ , then x < AND > y from x point of view.

Conclusion (2) is impossible by your observation; because you have no alternatives at all (you are using serial observation as an exclusive point of view, and cannot get __ from other points of view).

Furthermore, you continue to ignore the external point of view of __ and . , so here it is:

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.

 

[The Man]

No.

I observe ___ from more than a one and only one point of view.

So what, so can anybody else, but certain points of view have certain advantages like viewing the line segment perpendicular to your line of sight thus maximizing its apparent extents. In fact your claim of...

In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.

is the result of “one and only one point of view” that you call “parallel observation”.

So once again your denial of your use and dependence on exclusive points of view is in direct conflict with, well, your use and dependence on exclusive points of view. The problem is not with using exclusive points of view, they help us isolate aspects. The problem is with you saying no point of view is exclusive then depending entirely upon specific exclusive points of view as you clearly assert.

Non exclusive means that a conclusion about X is changed by different observations.

Observationally dependent conclusions are only the result of exclusive points of view. If those points of view did not exclude all other conclusions then the conclusion would not be dependent on the differences in the observations. Ideally the conclusions should be the same from all perspectives or points of view (by compensating for perspective dependent factors).

In the case of observation from x to y:

1) If x = . and y = ___ and the researched case is _._ , then x = y from x point of view.

2) If x = __ and y = . and the researched case is _._ , then x < AND > y from x point of view.

Conclusion (2) is impossible by your observation; because you have no alternatives at all (you are using serial observation as an exclusive point of view, and cannot get __ from other points of view).

You continue to delude yourself by not only depending on "one and only one" exclusive "parallel" point of view but by considering others as limited by your fallacies.

In the X Y Z coordinate system example I gave before with a line segment from coordinates (4, 3, 1) to (4, 3, 10) and in relation to a point at (4, 3, 5) one half of that line segment would have Z axis values < 5 and the other half >5. In other words it could be said that the line segment is”< AND >” the point in the Z axis. See by considering a line or line segment as defined by points your “< AND >” perspective dependent conclusion is no longer exclusive to your “parallel observation”.

Furthermore, you continue to ignore the external point of view of __ and . , so here it is:

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.You still do not understand the generalization, do you?

So now you want to introduce more exclusive points of view “external” and “internal” along with your own exclusive (incoherent and contradictory) conclusion to your notions where “no point of view is exclusive”. You still do not understand that by asserting “One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.” and then going to what you call an “external (objective) observation” you are utilizing exclusive points of view and now definitively asserting that “one and only one point of view” what you referred to as “external (objective) observation” is correct or as you put it “provide the correct knowledge about x or y.” If you can not make your subsequent posts consistent with your previous post then at least make some effort to have the end of some given post be consistent with its beginning.

 

[doronshadmi]

(4, 3, 5) one half of that line segment would have Z axis values < 5 and the other half >5. In other words it could be said that the line segment is”< AND >” the point in the Z axis.

No.

There are no half things in "< AND >" because ____ is an atom.

Since _____ is determined by you by coordinates (and any given coordinate is local by nature) you force them on the non-composed state of ____ , which causes you to use concepts like half line segments.

In other words, you are closed under Locality, as an exclusive point of view, that has no alternatives.

The rest of your post is nothing but locality as an exclusive point of view.

Some examples of Non-locality:

If the domain is . , then ____ is < AND > than . (notated as _._)

If the domain is . , then ____ is in AND out of . (notated as _._)

If the domain is [ ] , then ____ is in AND out of [ ] (notated as [_]_)


By your local exclusive point of view (where concepts like "half" are used), you cannot define Non-locality.


Analytic approach cannot be but a step-by-step serial observation, and your perception is limited to this thinking style.


As a result you have no chance (even if your life will be depended on it) to get Non-locality.

So now you want to introduce more exclusive points of view “external” and “internal” along with your own exclusive (incoherent and contradictory) conclusion to your notions where “no point of view is exclusive”.

Different alternatives of X cannot be considered as exclusive.

Only a Cyclops' view (like your view) is exclusive, exactly because X is observed from one and only one point of view (there are no alternatives).

 

[ddt]

If one travels some distance but ends up at the beginning is that progress? I guess in some sense.

That wholly depends on whether there's a singularity in the part of the plane that is bounded by the (Jordan) curve you traveled .

For the rest of the discussion: I see there's some kind of work division where everyone deconstructs one of doron's definitions. As I've not yet downloaded the UR.pdf document - which definition would you recommend me to take up?

 

[doronshadmi]

The Man,

Also you have missed the following:

_._ is not a combination of the two cases:

x = _

y = .

x < y (example: _ .)

or

x > y (example: . _)

More precisely:

((_ .) or (. _)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((__ .) and (. __)) is impossible.

Furthermore:

x = _

y = .

x = and > y (example: ._)

or

x < and = y (example: _.)

More precisely:

((_.) or (._)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((_.) and (._)) is impossible, because . cannot be both on (_.) and on (._)

In order to bat this impossibility let us use two line segments in different colors:

____

If . is on __ , than it is red

If . is on __ , than it is blue


It is quite trivial to understand that . cannot be red and blue

On the contrary, if ____ are in each other's domain, they can be both red AND blue (exactly as __ is in and out of . domain, but not vice versa)


By understanding Non-locality\Locality Interactions one concludes that Dedekind's cut of the rational numbers cannot satisfy the fact that given any R member on the real-line it cannot be considered as a limit for anything that is < or > than it.

 

[jsfisher]

** bump **

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

 

[Little 10 Toes]

Bump ditto (or is it ditto bump?)

I think you are overthinking things. Would you agree to the following definitions of the following terms:

• CardinalityWP: "In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3." Using the example set shown, I will use the notation |A| = 3 .
• SubsetWP: "In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide."
• Infinite: something that has no end or begining; something that cannot have a value attached to; unmeasurable/uncountable; unquantifiable. Example, the smallest/largest number; in geometry, a line. Synonym^WP: non-finite.
• Finite: something that does have an end; can have a value attached to; measurable/countable; practical; quantifiable. Example: the number of coins in my pocket, the number of grains of sand on a beach; in geometry, a line segment
• "Cannot be but": synonym of "then"

Do you agree to these definitions to the words?

If you only think about sets and subsets, and use "standard" mathematical "grammer", my definitions are the same as yours, just cleaner. Can you give me your definition of subset, proper subset, and the difference between the two without using examples until requested?

 

[doronshadmi]

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

By using a parallel observation of:

00
01
10
11

we are interested about the internal structure of this expression as the result of an whole\parts interaction.

From this point of view two basis structures are associated with each other, which are:

Symmetry (represented by 00 or 11)

Asymmetry (represented by 01 or 10)

Given any domain, Symmetry is not limited by it, for example:

Domain = []

Element = ___

Symmetry = [_]_ (simultaneously in and out)


Given any domain, Asymmetry is limited by it.

Domain = []

Element = ___

Asymmetry = [ ___ ] , [ ] ___ (not simultaneously in and out)

 

[jsfisher]

By using a parallel observation of:....

...which doesn't address any of my questions in the slightest. Care to try again?

 

[doronshadmi]

...which doesn't address any of my questions in the slightest. Care to try again?

Only if serial observation is the one and omly one point of view of the researched subject.

Care to try to use also parallel observation?

 

[jsfisher]

Only if serial observation is the one and omly one point of view of the researched subject.

Care to try to use also parallel observation?

You were taking shortcuts (again) with your notation, so I asked about it. Rather than simply answering directly, you wander off to some place irrelevant to the question.

Care to try again, or are you too busy on this random walk of yours?

 

[doronshadmi]

Some claims that 2 is both a member of the set of prime numbers AND the set of even numbers.

In this case 2 is non-local because it simultaneously belongs to two different sets.

This claim is wrong because an element is non-local only if it is related to another element by more than a one relation.

In that case 2 cannot be both a member and not a member of any given set; therefore 2 is local.

Actually, the whole idea of classes is limited by locality, because each researched thing must fully belong to a given class, or partially belong to it by using fuzzy logic's membership that is based on 0 to 1 value, which is itself local like any R member.

Non-locality holds only if a given thing is both 100% member AND not a member of a given domain, and this property is a strong mathematical framework.

By using analytic (serial only) observation, one must conclude that 100% member AND not a member is a contradiction or a weak framework like Paraconsistent Logic.

Both cases cannot get non-locality.

 

[doronshadmi]

You were taking shortcuts (again) with your notation, so I asked about it. Rather than simply answering directly, you wander off to some place irrelevant to the question.

Care to try again, or are you too busy on this random walk of yours?

My answer is direct to anyone who enables to use not only serial observation.

The bridge to get Organic Mathematics is in front of your mind. Only you can help yourself to see it and open yourself to new fundamental mathematical understanding.

You may say that I blame you in my inability to define my framework, but I really cannot help you to see things from parallel observation, because any observation is based on a direct perception of the observer.

If you get it you immediately understand what non-locality is, if you do not get it after 5 month dialog, you cannot get it.

 

[jsfisher]

Some claims that 2 is both a member of the set of prime numbers AND the set of even numbers.

Well, since 2 is both prime and even, it would be unreasonable to expect otherwise. Two is also an integer, positive, a solution to x^2 - 4 = 0, and a bunch of other things, too. Care to guess what that implies in terms of set membership?

By the way, are you claiming 2 is not both even and prime?

In this case 2 is non-local because it simultaneously belongs to two different sets.

First, since set membership is not a temporal phenomenon, the adverb simultaneously as no meaning in your statement.

Second, nothing you have suggested for your definition of non-local supports your statement.

This claim is wrong because an element is non-local only if it is related to another element by more than a one relation.

...which everything is, so everything must be non-local.

In that case 2 cannot be both a member and not a member of any given set; therefore 2 is local.

Even if your premises weren't faulty, there is no logical connection from them to this conclusion.

 

[jsfisher]

If you get you immediately understand what non-locality is, if you do not get if after 5 month dialog, you cannot get it.

Right. The chief should always blame the customers for the poor quality of the soup.