Deeper than primes

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Because the troll has learned that, when he comes back here, he gets fed. I warned them, I said, "Don't feed trolls - they'll learn to depend on you. Then how will they survive in the wild?"
 
doronshadmi said:
It has to be noted that Cardinality cannot be negative because it measures the existence of things, where the minimal measurement of existence is 0 (the measurement of non-existence).
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That's what I thought at first, and that's what anyone would think at first in my opinion, but what if you could?

I think some mathematicians have articulated such a weird concept.
http://answers.yahoo.com/question/index?qid=20070924105709AAbbzO1

There's antimatter(I don't know much about it but I had Physics and Chemistry so I know it exists). What if the mass of a particle, actually say it's greatest integer, equaled the number of elements in the set and electric charge density of a portion of the particle equaled the elements value. If it's antimatter, I think you'd have to have a negative number of elements.
 
Cardinality is about the existence of things, no matter if they are matter or anti-matter. In that case the cardinality of nothing is 0, and in the case of the empty set it refers to the existence of the sub-things that belong to the existing set (which is empty, in the case of the empty set).

Standard Math measures only the first level of the existence is sub-things in a given set, which is a partial measurement of the existence of the sub-things.

This partial measurement of existence is perfectly legal as long as it is understood as a partial measurement.

The problem starts when this partial measurement of things is taken as a universal principle of Set’s existence, and in that case we get an artificial limitation at the foundation of the mathematical branches that are based on the concept of Set.

OM’s notion is to deal with the complex relations of existing things by not fundamentally ignoring the properties that are used during these relations.

By following this approach one dose not ignore the internal complexity of any sub-thing that belongs to some set, because after all this internal complexity is used to distinguish between the members of some set, as can be seen in the case of S={ {{}}, {{a}}, {{a,b}}, {{b}}, ... , {{a,b,c,...}}, ...}.

The magnitude of S measurement can’t be found if the internal complexity of each member of set S is ignored, so after all the number of members of set S is inseparable of that complexity.

When this notion is generalized, then we find ourselves dealing with the existence of the measured members of some set (S in this example).

In other words the relations between the properties that are used in order to measure something must first be understood, and then, by careful treatment, we can ignore some of them according to some systematic reasoning, but the knowledge of the general state is always in our mind and helps us to understand better our chosen limited navigations at the basis of some research.
 
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dlorde said:
And mostly pointless...
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No, it is exactly the linkage between local things like points and non-local things line lines (where the existence of non-local things like lines is independent of the existence of local things like points, and vice versa).

Non-locality and Locality are a universal principle that holds between any n-dim and k-dim, such that:

n-dim = 1 to ∞
k-din = 0 to ∞

A point is the simplest example of Locality and a line is the simplest example of Non-locality, and they can be used to understand Non-locality\Locality Linkage Without a Loss of Generality.

Both of them are two aspects of a one atomic state that enables the linkage between them, and the result is the complexity that we observe both in our abstract and physical realm.
 
power2012 said:
Yeah I've heard of there being "right brain" thinking, as opposed to "left brain" thinking
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The idea is to develop useful mathematical activity that can complement the verbal-based serial stap-by-step "left-brain" thinking style.
 
Pure_Argent said:
Because the troll has learned that, when he comes back here, he gets fed. I warned them, I said, "Don't feed trolls - they'll learn to depend on you. Then how will they survive in the wild?"
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How you survive in the wild Pure_Argent?
 
The Man said:
That you choose to restrict your “measurement of existence” to the natural numbers
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Cardinality is not limited to natural numbers, Cardinality is the measurement of the existence of things that does not ignore their internal complexity (this ignorance is Standard Math's basic approach, and I clearly exposed it) .
 
doronshadmi said:
Cardinality is not limited to natural numbers, Cardinality is the measurement of the existence of things that does not ignore their internal complexity (this ignorance is Standard Math's basic approach, and I clearly exposed it) .
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No, that is Doronality. You've been told before; don't use an existing term to name a concept you have defined (however poorly).
 
zooterkin said:
No, that is Doronality. You've been told before; don't use an existing term to name a concept you have defined (however poorly).
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Do not use a limited viewpoint of X as its universal state, and measuring the first level of existence of members, is a limited use of Cardinality, simply becaue the internal form of each member is not ignored during measurment.
 
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The Man,

Do you agree that a line exists even if points do not exist?

Do you agree that a point exist even if a line does not exist?
 
If we translate the word “definition” to Hebrew we get the word “hagdara”.

“hagdara” is based on the root g.d.r that is common with the Hebrew word “gader” .

The translation of the word “gader” to English is “fence”, where the abstract meaning in this case is “the thing that is used for limitation”.

By following this notion, a definition is a limitation of already existing thing that enables us to use it for our purpose.

By following this reasoning the current mathematical activity does not deal with the existence of things but with the possible manipulations of already existing things.

OM is a pre-definition framework because it deals with the existence of things.

From this pre-definition view a non-local thing has the property to belong AND not to belong to a given limitation (some domain) where a local thing has the property to belong XOR not to belong to a given limitation (some domain).

The minimal representation of Locality is a point and if it is used as a common thing for at least two different things, then it must belong to both of them.

This is not the case with a line, which can belong AND not to belong to these two different things, even if it is common for both of them, for example:



Code: 
+------+
|     \|
|      \
|      |\
+------+-\----+
       |  \   |
       |      |
       |      |
       +------+

The linkage between Non-locality and Locality stands at the basis of the researchable mathematical entities.
 
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doronshadmi said:
If we translate the word “definition” to Hebrew we get the word “hagdara”.

“hagdara” is based on the root g.d.r that is common with the Hebrew word “gader” .

The translation of the word “gader” to English is “fence”, where the abstract meaning in this case is “the thing that is used for limitation”.

By following this notion, a definition is a limitation of already existing thing that enables us to use it for our purpose.

By following this reasoning the current mathematical activity does not deal with the existence of things but with the possible manipulations of already existing things.

OM is a pre-definition framework because it deals with the existence of things.

From this pre-definition view a non-local thing has the property to belong AND not to belong to a given limitation (some domain) where a local thing has the property to belong XOR not to belong to a given limitation (some domain).

The minimal representation of locality is a point and if it is used as a common thing for at least two different things, that it must be belong to both of them.

This is not the case with a line, which enables to belong AND not to belong to these two different things.

The linkage between Non-locality and Locality stands at the basis of the researchable mathematical entities.
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I can't help but reply.
Doron, this is certainly the clearest post you've made in this thread of the heart and intent of OM.
I mean that for the first time reader who has no background in math or mysticism, you cut right to the chase.

OM is a pre-definition framework because it deals with the existence of things.
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This itself is a very concrete example of OM thinking.
a "pre-definition framework" seems oxymoronic, because you do define in OM, and you do have a frame.

The intent is to be able to say, "Here's my movable, porous, impermanent frame."
"Here's the landscape before I start boxing things in."
But, of course, even the manipulation of objects or elements in the landscape depends on existing them, so to speak.

So you stand on the "fence," by asserting that the "researchable" does depend on an interaction of both definition (Locality) and the Undifferentiated (Non-Locality)

Your program posits the pre-existence (as regards any mental conception) of pre-existing, individual elements and a movable frame that only takes them in as a shifting viewpoint.

You see, of course, that this approach, this interaction of two fundamental ("atomic" as you say) principles does define the discourse
and has mathematical and intellectual consequences.

I'm fascinated by the contrast of assumptions in Doron Vs. Traditional Mathematics.
You do bring to view some "hidden assumptions."
 
doronshadmi said:
Cardinality is not limited to natural numbers, Cardinality is the measurement of the existence of things that does not ignore their internal complexity (this ignorance is Standard Math's basic approach, and I clearly exposed it) .
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Then integers or real numbers would be acceptable measurements “of the existence of things” in your notion of Doronality?
 
The Man said:
Then integers or real numbers would be acceptable measurements “of the existence of things” in your notion of Doronality?
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No, it is exactly as the current measurement where the internal complexity of the measured member is not unconditionally ignored (as the standard approach does).

As for measurement of infinite collections, their cardinality is incomplete (based on different proportions) exactly because any amount of infinitely many players has no fixed value from one hand (as finitely many players has) and they can’t be the stage, which is the thing that has no successor (any collection of infinite players has a successor even if it is not an immediate successor).

As for absolute real numbers and absolute non-local numbers, by further research they may be used as Cardinalities, but a further research is needed here to carefully investigate the consistency and validity of this notion.
 
Apathia said:
I can't help but reply.
Doron, this is certainly the clearest post you've made in this thread of the heart and intent of OM.
I mean that for the first time reader who has no background in math or mysticism, you cut right to the chase.



This itself is a very concrete example of OM thinking.
a "pre-definition framework" seems oxymoronic, because you do define in OM, and you do have a frame.

The intent is to be able to say, "Here's my movable, porous, impermanent frame."
"Here's the landscape before I start boxing things in."
But, of course, even the manipulation of objects or elements in the landscape depends on existing them, so to speak.

So you stand on the "fence," by asserting that the "researchable" does depend on an interaction of both definition (Locality) and the Undifferentiated (Non-Locality)

Your program posits the pre-existence (as regards any mental conception) of pre-existing, individual elements and a movable frame that only takes them in as a shifting viewpoint.

You see, of course, that this approach, this interaction of two fundamental ("atomic" as you say) principles does define the discourse
and has mathematical and intellectual consequences.

I'm fascinated by the contrast of assumptions in Doron Vs. Traditional Mathematics.
You do bring to view some "hidden assumptions."
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Dear Apathia,

When we close things under definitions we have to ask ourselves how they are still related to each other.

OM's solution is "the dance between the closed (local) and the unclosed (non-local) that creates the non-trivial complexity of both abstract and non-abstract of a one organic realm.

By this approach we get a non-total framework that is the result of the linkage between two totalities, which are opened to each other in order to create a non-total offspring (and therefore non-trivial complex) realm, which is richer than its total parents.
 
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doronshadmi said:
No, it is exactly as the current measurement where the internal complexity of the measured member is not unconditionally ignored (as the standard approach does).
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Once again you simply misrepresent the notion of cardinality.

All ignorance is conditional, specificaly upon that which is being ignored and why it can be ignored in some specifc consideration.

doronshadmi said:
As for measurement of infinite collections, their cardinality is incomplete (based on different proportions)
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Incomplete proportions?


doronshadmi said:
exactly because any amount of infinitely many players has no fixed value from one hand (as finitely many players has) and they can’t be the stage, which is the thing that has no successor (any collection of infinite players has a successor even if it is not an immediate successor).
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Are you forgetting that you notion of “any collection” includes “the stage”? remember…


doronshadmi said:
...(without it you simply unable to collect players).
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If any such “collection” “has a successor” then so too does that particular “stage” you used “to collect players”.


doronshadmi said:
As for absolute real numbers and absolute non-local numbers, by further research they may be used as Cardinalities, but a further research is needed here to carefully investigate the consistency and validity of this notion.
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Well the further investigation on this thread continues to demonstrate your notions as both inconsistent and invalid, particularly when addressing that “standard approach”.
 
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