Deeper than primes

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doronshadmi said:
So by your jargon Cardinality and Cardinal are not the same thing, ok got it.

Cardinality X = the object that has X as its cardinal.

In this case Cardinality 0 = { } = the object that has 0 as its cardinal.

But you see The Man, since I use Cardinal as the measurement unit of existence of the measured things, where a set is nothing but the measurement tool, than the resulted value is not about the measurement tool but about the measured things.

Again you do not follow OM, and in this case I am in my yard you are in your yard, and there is silence between us.
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Well that is the problem Doron, as I tried to explain before, your whole ‘Cardinal as the measurement unit of existence’ concept. When your set B has the empty set as its only member and you use the Cardinal of B ‘as the measurement unit of existence’ it is still only the cardinality of B (a set with a member) and has no bearing on the empty set (a set with no members). Again you do not follow OM and that is understandable as ‘your yard’ is just a mess of convolutions, mountains from molehills and pits of contradiction. Certainly there is no “silence between us” as you keep yelling how great your yard is compared with ours as you scurry around those convolutions, over those mountains from molehills and inevitably fall into one of your pits of contradiction, while we keep yelling for you to ‘clean up your yard’.
 
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The Man said:
Well that is the problem Doron, as I tried to explain before, your whole ‘Cardinal as the measurement unit of existence’ concept. When your set B has the empty set as its only member and you use the Cardinal of B ‘as the measurement unit of existence’ it is still only the cardinality of B (a set with a member) and has no bearing on the empty set (a set with no members).
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The Man said:
Is there anything in particular you are assuming that I missed in that post, other then, well, just more assumptions on your part?
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According to OM, Cardinal is the sum of the things that are measured by a measurement tool, where the measurement tool is excluded.

I call this sum the magnitude of the existence of the measured things.

By following this ontological notion, we get for example:



A={ }

|A| = |{ }| = 0 = the magnitude of existence of Emptiness, where A is a measurement tool (value 0 is about Emptiness and not about A).

The cardinal of A is the measurement results about Emptiness.



B={A}

|B| = |{A}| = 1 = the magnitude of existence of A, where B is a measurement tool (value 1 is about A and not about B).

The cardinal of B is the measurement results about A.



C={A,B}

|C| = |{A,B}| = 2 = the magnitude of existence of A,B where C is a measurement tool (value 2 is about A,B and not about C).

The cardinal of C is the measurement results about A,B.



Do you get it?
 
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doronshadmi said:
According to OM, Cardinal is the sum of the things that are measured by a measurement tool, where the measurement tool is excluded.

I call this sum the magnitude of the existence of the measured things.

By following this ontological notion, we get:

A={ }
|A| = |{ }| = 0 = the magnitude of existence of Emptiness, where A is a measurement tool (value 0 is about Emptiness and not about A).

The cardinal of A is the measurement results about Emptiness.


B={A}
|B| = |{A}| = 1 = the magnitude of existence of A, where B is a measurement tool (value 1 is about A and not about B).

The cardinal of B is the measurement results about A.


C={A,B}
|C| = |{A,B}| = 2 = the magnitude of existence of A,B where C is a measurement tool (value 2 is about A,B and not about C).

The cardinal of C is the measurement results about A,B.

Do you get it?
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Doron I got it when you posted it before and as I said before it is just a contrivance, a lie, a way for you to shift the value of your “magnitude of existence” by one so it agrees with your notions. You only take the cardinality of your “measurement tool” and never what you claim you are measuring “the magnitude of existence” of the set that must become a member of some other set for you to measure, where you only measure the cardinality of that other set and claim it relates to that subset.
 
The Man said:
Doron I got it when you posted it before and as I said before it is just a contrivance, a lie, a way for you to shift the value of your “magnitude of existence” by one so it agrees with your notions. You only take the cardinality of your “measurement tool” and never what you claim you are measuring “the magnitude of existence” of the set that must become a member of some other set for you to measure, where you only measure the cardinality of that other set and claim it relates to that subset.
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What do you mean by lie?

By OM the cardinal is an ontological value of the measured things, where the measurement tool is excluded.

By this notion we get exactly the same result of the standard notion, but by using an ontological notions we can develop the framework beyond the abilities of the standard notion, as I clearly show in http://www.geocities.com/complementarytheory/OMPT.pdf .

I suggest you to not take the path of "you are a liar because you do not think like me" poor style.

Once again:

The Man said:
Who are you calling a ‘Ho’?

“ “ is not a description it is a space in quotation marks, { } is not a description it is a space between brackets. Both of those are representations, what follows them in the previous statement are descriptions as this statement is also a description of that statement. Representations are not descriptions, but require descriptions in order to indicate exactly what it is you’re trying to represent. You have plenty of representations, Doron, and very few descriptions.
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I am talking on the level that tries to get the very existence of things (ontology), you are talking on the level that tries to get the descriptions of already existing things (their definitions).

From the level of ontology " " is an existing (empty) description exactly as { } is an existing (empty) set.

The cardinal of some set is determined by the sum of the things that belong to this set.

EDIT:

By using the ontological view one enables to distinguish between the empty set and the full set, where the cardinal of the set (called the empty set) that measures Emptiness < the sum of any collection of members, and the cardinal of the set (called the full set) that measures Fullness > the sum of any collection of members.

Only the full set is considered as actual infinity and as a result any non-finite collection is incomplete and it does not have a crisp cardinal value.
 
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Doron,

Is "ontological" now the latest of favorite words? I would have thought you'd have stuck with "fusion" for at least another day or two. And think of poor "distinction" and "interaction" - both ignored for oh so long.

At any rate, I've added "ontological" to the list of words and phrases you don't understand.
 
jsfisher said:
Doron,

Is "ontological" now the latest of favorite words? I would have thought you'd have stuck with "fusion" for at least another day or two. And think of poor "distinction" and "interaction" - both ignored for oh so long.

At any rate, I've added "ontological" to the list of words and phrases you don't understand.
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Please provide some detailed examples taken from my work that support your claim.
 
doronshadmi said:
So by your jargon Cardinality and Cardinal are not the same thing, ok got it.
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Kettle, have you met Pot? The "jargon" that jfisher and The Man (I assume you're talking to them both) are using are terms that most math students know. You're the one that is taking standard terms and using them for your ideas.

Do you use this definition of cardinality, "In mathematics, the cardinality of a set is a measure of the 'number of elements of the set' "? Simple question. (Definition shamelessly stolen from wikipedia).

Please note it does not talk about the "magnitude". It only refers to the number of elements/atoms/urelements/objects (they all mean the same thing) in a set.

doronshadmi said:
Cardinality X = the object that has X as its cardinal.
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But you're not referring to the object. You could be talking about the empty set or a non-empty set. (Whoops, there I go again. How do I know if you're referring to an element or a set?)

doronshadmi said:
In this case Cardinality 0 = { } = the object that has 0 as its cardinal.
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So if you're talking about a set, then you are referring to a set that has no elements/atoms/urelements/objects. If not, then how can an object have a cardinality to it? Also notice how { } is empty, meaning nothing is in there.

doronshadmi said:
But you see The Man, since I use Cardinal as the measurement unit of existence of the measured things, where a set is nothing but the measurement tool, then the resulted value is not about the measurement tool but about the measured things.
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Well something either exists or it doesn't.

Is this your "magnitude of existance" scale?
0 = it doesn't exist
1 = it exists
2 = it really exists
3 = it really, really exists
4 = it really, really, really, exists
(Ad infinitum or Ad nauseam, your choice)

Also, if "a set is nothing but the measurement tool, then the resulted value is not about the measurement tool but about the measured things", then a perfect analogy is that a set is a ruler. It does not contain anything.

doronshadmi said:
This is exacly the case of |{ }|, which is the measurment unit of what belongs to { }.
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No. Cardinality does not measure what belongs to what. It only counts the number of what things that are in a set.

doronshadmi said:
Again you do not follow my arguments, and in this case I am in my yard you are in your yard, and there is silence between us.
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You are correct since you keep changing words and their meanings, and adding new words that you don't define. Oh, and that yard that you're not in, it's bigger, has more people, and there's a party going on.
 
Little 10 Toes said:
Kettle, have you met Pot? The "jargon" that jfisher and The Man (I assume you're talking to them both) are using are terms that most math students know. You're the one that is taking standard terms and using them for your ideas.

Do you use this definition of cardinality, "In mathematics, the cardinality of a set is a measure of the 'number of elements of the set' "? Simple question. (Definition shamelessly stolen from wikipedia).

Please note it does not talk about the "magnitude". It only refers to the number of elements/atoms/urelements/objects (they all mean the same thing) in a set.

But you're not referring to the object. You could be talking about the empty set or a non-empty set. (Whoops, there I go again. How do I know if you're referring to an element or a set?)

So if you're talking about a set, then you are referring to a set that has no elements/atoms/urelements/objects. If not, then how can an object have a cardinality to it? Also notice how { } is empty, meaning nothing is in there.

Well something either exists or it doesn't.

Is this your "magnitude of existance" scale?
0 = it doesn't exist
1 = it exists
2 = it really exists
3 = it really, really exists
4 = it really, really, really, exists
(Ad infinitum or Ad nauseam, your choice)

Also, if "a set is nothing but the measurement tool, then the resulted value is not about the measurement tool but about the measured things", then a perfect analogy is that a set is a ruler. It does not contain anything.

No. Cardinality does not measure what belongs to what. It only counts the number of what things that are in a set.

You are correct since you keep changing words and their meanings, and adding new words that you don't define. Oh, and that yard that you're not in, it's bigger, has more people, and there's a party going on.
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Please start by looking at:

http://www.internationalskeptics.com/forums/showpost.php?p=4656373&postcount=2547

http://www.internationalskeptics.com/forums/showpost.php?p=4656629&postcount=2551

I think that you will find there my answers to your questions.

EDIT:

As about existence, I wish to add this:

The "members" of {} do not exist (the set is used to measure Emptiness).

The members of {a,b,c,…} are partially exist (the set is used to measure a collection).

The "members" of {_}_ are fully exist (the set is used to measure Fullness).

Since the current paradigm of set is not based on ontological viewpoint, the full set cannot be understood, and therefore it is not used by the standard paradigm.

OM changes this situation by providing a rigorous ontological basis to the full set.
 
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doronshadmi said:
I think that you will find there my answers to your questions.
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You think wrong.

You still have the foundational issue to deal with. Nothing matters after that since you have built your house of cards on a false assertion.
 
doronshadmi said:
What do you mean by lie?
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A deception, a falsehood, an untruth, something intended or serving to convey a false impression, an imposture, an inaccurate or false statement.

doronshadmi said:
By OM the cardinal is an ontological value of the measured things, where the measurement tool is excluded.
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Your measurement tool is not ‘excluded’ because that is what you are ‘measuring’ by taking its cardinality, and quite deliberately, which again makes your ‘measurement’ a lie, a deception, a falsehood, an untruth, something intended or serving to convey a false impression, an imposture, an inaccurate or false statement. Not to mention your claim that your measurement tool is ‘excluded’


doronshadmi said:
By this notion we get exactly the same result of the standard notion, but by using an ontological notions we can develop the framework beyond the abilities of the standard notion, as I clearly show in http://www.geocities.com/complementarytheory/OMPT.pdf .
Click to expand...

No Doron the standard notion is that the cardinality of a set is, well, the cardinality of that set, not of some subset of that set. Also not forcing the empty set to have a member you call ‘fusion’ so that it is, well, not empty.


doronshadmi said:
I suggest you to not take the path of "you are a liar because you do not think like me" poor style.
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I suggest you take the path of honesty in your notions, stop lying to yourself, trying to lie to us and just ‘clean up your yard’


doronshadmi said:
Once again:


I am talking on the level that tries to get the very existence of things (ontology), you are talking on the level that tries to get the descriptions of already existing things (their definitions).

From the level of ontology " " is an existing (empty) description exactly as { } is an existing (empty) set.

The cardinal of some set is determined by the sum of the things that belong to this set.

EDIT:

By using the ontological view one enables to distinguish between the empty set and the full set, where the cardinal of the set (called the empty set) that measures Emptiness < the sum of any collection of members, and the cardinal of the set (called the full set) that measures Fullness > the sum of any collection of members.

Only the full set is considered as actual infinity and as a result any non-finite collection is incomplete and it does not have a crisp cardinal value.
Click to expand...

Again just more baseless assumptions, misunderstanding, misrepresentation and blatant falsehoods on your part, it is your typical word salad.
 
jsfisher said:
Doron,

Is "ontological" now the latest of favorite words? I would have thought you'd have stuck with "fusion" for at least another day or two. And think of poor "distinction" and "interaction" - both ignored for oh so long.

At any rate, I've added "ontological" to the list of words and phrases you don't understand.
Click to expand...


Let's not forget the oldies like 'local', 'non-local' and 'complementation' and of course my all time favorite 'mutual independence'
 
doronshadmi said:
OM changes this situation by providing a rigorous ontological basis to the full set.
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Another word for the list.

Nothing in your organic mathematics presentations have been rigorous by even the most generous interpretation of the word, nor have then been ontological. They have been contradictory, though, so at least you can take some credit for that. Unfortunately, the notions you attempt to conceive are unnecessary and contrived. They have no value whatsoever.
 
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