Deeper than primes

[ddt]

Oh, and look at this thread at ToeQuest.

 

[doronshadmi]

Oh, and look at this thread at ToeQuest.

ddt tries to hijack the dialog of this thread to another forum.

I suggest to avoid from him in doing it.

Generally ddt is obsessed about my actions in the internet and makes an history list of these actions.

 

[The Man]

No, B is an existing measurement tool that measures the existence of its members, whether they are fusions (in the case of Emptiness or Fullness) or collections (in the case of A).

Regardless of whatever you might think you are saying above it does not change the fact that your “measurement of existence” is only a measurement of your set B and not what you are asserting it as, a measurement of set A as the set in the axiom of the empty set.

Nothing is circular here as long as you distinguish between the EXISTING measurement tool {X} and |{X}|, where |{X}| is the measurement's result of X (where X is a fusion in the case of Emptiness or Fullness, or X is a collection in the case of A).

.

I did not claim them to be circular since, as I said before, your ‘measurement’ of set your B is not what you assert you are measuring as set A. I simply claimed that it was crap. However I am sure jsfisher and I can agree to a collection of those two descriptive terms resulting in their fusion into the appropriate phrase ‘circular crap’.

This is exactly what the ZF axiom of the empty set does.

It defines the empty set by the absence of collections where "absence of collections" is exactly the fusion known as Emptiness.

Are you claiming that the empty set is empty? How enlightened of you. As for the other gibberish about “fusion known as Emptiness” that seems to be coming from some bizarre fusion of neurons in your head.

Furthermore, the axiom of the empty set does not determine the existence of the empty set because by the ZF axiom of the empty set:

"There exists set A such that any set (including A, or in other words, A exists independently of the axiom's description) is not a member of A"

So you simply do not understand what an axiom is, how surprising.

Pay attention to the fact that if A exists because of the axiom of the empty set, then we are using a circular reasoning, where A existence depends on A existence (also please pay attention to the fact that if A is not one the things that are not members of A, then A is not empty).

Well it specifically says that ‘no set’ is a member of A (which is a set), did you pay attention to that?

In order to avoid this circularity, A must exist independently of the axiom, which only describes its properties and does not determine its existence.


So "There exists set A" is a fact of existence that does not depend on the description of the ZF axiom of the empty set, and A existence is used to measure "the absence of collections", which is exactly the fusion known as Emptiness.

You really don’t understand the meaning of an axiom, do you? Just as you do not get to simply change the meaning of cardinality to suit your whim; likewise you do not get to change the meaning of axiom or the meaning of an axiom like the axiom of empty set. You what to present your notions? Then start by writing down your axioms as well as clearly defining your terms and stop this crap where you just apply your own bizarre and obscure meaning to well established terms, phrases, concepts, notation and axioms.

 

[jsfisher]

You don't understand what a Set is as long as you do not distingush between collection and fusion.

Nonsense. That's the fantasy world you have created for yourself. You can't even define your latest additions to your vocabulary in any coherent way. Add to that, all of your notions are without necessity. They serve no purpose whatsoever.

The rest of us are quite comfortable with Set Theory as provided by Mathematics. We have no need for your undefined and misused terminology, your circular logic, your gibberish, nor your contradictions.

 

[jsfisher]

Since cardinality measures the existence of things...

Nonsense! You made that up. Just because you have no clue what cardinality really means, that doesn't give you the privilege of using it in any arbitrary way you like.

 

[ddt]

ddt tries to hijack the dialog of this thread to another forum.

Strangely, you're claiming that over on ToeQuest too. So which is it?

I suggest to avoid from him in doing it.

What does that mean? Please write understandable English.

Generally ddt is obsessed about my actions in the internet and makes an history list of these actions.

Someone's got to do the dirty work . I'm just helping the more gullible, or more easily impressed people to see your writings for what they are. I've tried discussing with you, to no avail, as you won't answer pertinent questions anyway - and I'm not as patient as jsfisher or The_Man.

 

[doronshadmi]

There is a description.

It can be empty for example " ", or it can be non-empty for example "There exists set A such that …".

The existence of a description does not depend on its content.

On the contrary, the property of a description depends on its content.

The same holds in the case of the ZF axiom of the empty set.

This axiom determines the property of already existing thing, where this existing thing is used to determine the magnitude of existence (the cardinality) of its members.

A more general viewpoint about Sets:

Set is a form of collection, which its members can be collections or their absence (where "the absence of collections" is the particular case of the fusion called Emptiness)

If the member of a set is a collection, then the magnitude of the existence of the member is at least 1.

If the member is a fusion, then the magnitude of the existence of the member is at least 0.

As about collections and fusions, this time real read http://www.internationalskeptics.com/forums/showpost.php?p=4652231&postcount=2483 including th link to Michael Potter's book.

If you don't wish to do that, then your ignorance about collections and fusions is your free choice.

 

[jsfisher]

If you don't wish to do that, then your ignorance about collections and fusions is your free choice.

There are merely things you have made up to suit your own fantasy. You have not demonstrated any significance for them.

 

[doronshadmi]

There are merely things you have made up to suit your own fantasy. You have not demonstrated any significance for them.

No, you jsfisher, do not find any significance for them.

On the contrary I clearly show in http://www.internationalskeptics.com/forums/showpost.php?p=4652231&postcount=2483 how the distinction between collections and fusions has a profound influence on fundamental things like, for example, the universal quantifier.

In page 22 of Michael Potter's book we find this paragraph:

And what if we try to make something out of nothing? A container with nothing in it is still a container, and the empty collection is correspondingly a collection with no members. But a fusion of nothing is an impossibility: if we try to form a fusion when there is nothing to fuse, we obtain not a trivial object but no object at all.

Empty fusion = "no fusion at all"

Empty collection ≠ "no collection at all"

So in the case of the empty set, the absence of members is defined in terms of fusions, or more precisely, in terms of Empty fusion.

It can be done only if "no fusion at all" is addressed in terms of Set's membership, because "fusion of nothing" is "an impossibility" on its own (if it is not addressed in terms of membership by an existing collection, known as Set)..

 

[The Man]

There is a description.

It can be empty for example " ", or it can be non-empty for example "There exists set A such that …".

The existence of a description does not depend on its content.

On the contrary, the property of a description depends on its content.

A description that does not describe anything is not a description, thus a description is dependent on content (that it describe something) in order to exist as, well, a description.

The same holds in the case of the ZF axiom of the empty set.

This axiom determines the property of already existing thing, where this existing thing is used to determine the magnitude of existence (the cardinality) of its members.

Again with the misunderstanding and misrepresentation of the axiom of empty set. That axiom defines one thing, surprisingly, the empty set. The rest of this malarkey is just your usual meaningless drivel that has absolutly nothing to do with what you're trying to ascribe it to, specifically in this case the axiom of empty set.

A more general viewpoint about Sets:

Set is a form of collection, which its members can be collections or their absence (where "the absence of collections" is the particular case of the fusion called Emptiness)

If the member of a set is a collection, then the magnitude of the existence of the member is at least 1.

If the member is a fusion, then the magnitude of the existence of the member is at least 0.

As about collections and fusions, this time real read http://www.internationalskeptics.com/forums/showpost.php?p=4652231&postcount=2483 including th link to Michael Potter's book.

If you don't wish to do that, then your ignorance about collections and fusions is your free choice.

The empty set has no members, that’s its meaning. Why do you continue to try and spew this crap where you insist on giving the empty set some member that you refer to as ‘fusion’, (whatever that is suppose to mean to you) or take the ‘cardinality’ of some set that only has the empty set as a member as some ‘measure its existence’, which is still just the ‘cardinality’ of that other set and has noting to do with the empty set itself?

Doron, if you can not accurately describe your use of “collections and fusions” in simple and straight forward terms right here on this thread then the ignorance remains yours. So although you might have read about them in whatever reference you are citing, your history clearly demonstrates that you will apply your own unique and bizarre interpretations and meaning in spite of references you provide. Asking people to waste their time reading your reference when you will typically not adhere to the implications of that reference yet assert some other meaning altogether, again only displays your belief that others are as ignorant as you.

 

[The Man]

No, you jsfisher, do not find any significance for them.

On the contrary I clearly show in http://www.internationalskeptics.com/forums/showpost.php?p=4652231&postcount=2483 how the distinction between collections and fusions has a profound influence on fundamental things like, for example, the universal quantifier.

In page 22 of Michael Potter's book we find this paragraph:



Empty fusion = "no fusion at all"

Empty collection ≠ "no collection at all"

So in the case of the empty set, the absence of members is defined in terms of fusions, or more precisely, in terms of Empty fusion.

It can be done only if "no fusion at all" is addressed in terms of Set's membership, because "fusion of nothing" is "an impossibility" on its own (if it is not addressed in terms of membership by an existing collection, known as Set)..

Well thanks Doron, for demonstrating, as usual, you will not adhere to clear statements and inferences of your own reference, but just make up your own bizarre and meaningless interpretation.

 

[jsfisher]

On the contrary I clearly show...

Yet another word for which Doron has his own private meaning.

 

[ddt]

No, you jsfisher, do not find any significance for them.

On the contrary I clearly show in http://www.internationalskeptics.com/forums/showpost.php?p=4652231&postcount=2483 how the distinction between collections and fusions has a profound influence on fundamental things like, for example, the universal quantifier.

In page 22 of Michael Potter's book we find this paragraph:



Empty fusion = "no fusion at all"

Empty collection ≠ "no collection at all"

So in the case of the empty set, the absence of members is defined in terms of fusions, or more precisely, in terms of Empty fusion.

It can be done only if "no fusion at all" is addressed in terms of Set's membership, because "fusion of nothing" is "an impossibility" on its own (if it is not addressed in terms of membership by an existing collection, known as Set)..

You have yet to show any value of this all. This whole "fusion" thing seems conspicuously absent in the more mathematical parts of Potter's book, judging by the wiki page on Scott-Potter set theory^WP. So we're waiting with baited breath to see you show the "profound influence" it has on the universal quantifier. I can't wait to see how you're going to butcher that - thus far you've shown only utter miscomprehension of the notion of axiomatization. Oh, and I see you've managed to misrepresent category theory in the mean time too. Bravo!

 

[doronshadmi]

A description that does not describe anything is not a description, thus a description is dependent on content (that it describe something) in order to exist as, well, a description.

Ho yes it is.

" " is an existing (empty) description exactly as { } is an existing (empty) set.

Again with the misunderstanding and misrepresentation of the axiom of empty set. That axiom defines one thing, surprisingly, the empty set.

The axiom describes the property of the empty set, and it does not determine its existence.

The empty set has no members, that’s its meaning.

Exactly, and this meaning is achieved only by using the notion of fusion as a member of the empty set and not the notion of collection as the member of the empty set.

Empty fusion = = the absence of collections and\or fusions

Empty collection = { }

It is clearly shown that the members of { } are defined in terms of Empty fusion and not in terms of Empty collection.

Why do you continue to try and spew this crap where you insist on giving the empty set some member that you refer to as ‘fusion’, (whatever that is suppose to mean to you) or take the ‘cardinality’ of some set that only has the empty set as a member as some ‘measure its existence’,…

Cardinality value can be taken only by using a collection.

A collection (whether it is empty or not, it does not matter) is first of all an existing thing, that in the case of Cardinality it is used as a tool to determine the magnitude of the existence of the possible members that belong to it. these members can be collections, fusions where fusions can be empty ({ }) or full( {_}_ }.

which is still just the ‘cardinality’ of that other set and has noting to do with the empty set itself ?

Again, the value of a cardinal is determined by the magnitude of the existence of some set's members, so in the case of B={A}, |{A}| determinates the magnitude of the existence of A, which in this case it is the member of B.

If some set has more than a one existing member, then the velue of that cardinal is the sum of the the existing members.

Doron, if you can not accurately describe your use of “collections and fusions” in simple and straight forward terms right here on this thread then the ignorance remains yours. So although you might have read about them in whatever reference you are citing, your history clearly demonstrates that you will apply your own unique and bizarre interpretations and meaning in spite of references you provide. Asking people to waste their time reading your reference when you will typically not adhere to the implications of that reference yet assert some other meaning altogether, again only displays your belief that others are as ignorant as you.

I write my terms in simple and straight forward way right here on this thread.

Your history clearly demonstrates that your rough thinking cannot get the outcomes of a fine thinking.

 

[doronshadmi]

Well thanks Doron, for demonstrating, as usual, you will not adhere to clear statements and inferences of your own reference, but just make up your own bizarre and meaningless interpretation.

Thank you The Man for your rough thinking. It helps me a lot to re-think about my notions in order to find out how they can be clarified.

In this case you simply do not get the beautiful abstract notion, that the member of { } is exactly the Empty fusion, and this is exactly the reason of why the cardinality of the members of the empty set is 0.

 

[jsfisher]

The axiom describes the property of the empty set, and it does not determine its existence.

Let's do a fact check on doron's assertion. Here, in its full simplicity, is the Axiom of the Empty Set:

[latex]$$$ \exists x\, \forall y\, \lnot (y \in x) $$$[/latex]​

Now, since Doron doesn't "do" math, we can translate the axiom into basic English:

There exists a set that has no members.​

You are wrong again, Doron.

 

[doronshadmi]

Oh, and I see you've managed to misrepresent category theory in the mean time too. Bravo!

Please give some concrete example.

 

[doronshadmi]

Let's do a fact check on doron's assertion. Here, in its full simplicity, is the Axiom of the Empty Set:

[latex]$$$ \exists x\, \forall y\, \lnot (y \in x) $$$[/latex]​

Now, since Doron doesn't "do" math, we can translate the axiom into basic English:

There exists a set that has no members.​

You are wrong again, Doron.

http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500

 

[jsfisher]

In this case you simply do not get the beautiful abstract notion, that the member of { } is exactly the Empty fusion...

You cite a reference for you latest vocabulary addition that clearly states the "empty fusion" is impossible, then you proceed to use this impossibility as an actual object. Not only that, you use it as a member of a member-less set.

Are you still confused why we regard many of your statements as contradictory?

...and this is exactly the reason of why the cardinality of the members of the empty set is 0.

I'll leave identifying the absurdities of this part of the statement as an exercise for the interested reader.

 

[ddt]

Please give some concrete example.

There's this English proverb containing the nouns "pearls" and "swine".