Deeper than primes

[Little 10 Toes]

Nice try, he didn't.

Oh yes he did.

No he didn't. What he wrote is irrelevant because Cardinality is the unit measurement of the existence of things, whether he likes it or not.

First, see above. Secondly, to quote Inigo Montoya, "You keep using that word. I do not think it means what you think it means."

• Wikipedia: In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
• Dictionary.com: (of a set) the cardinal number indicating the number of elements in the set.
• Wiktionary: (set theory) Of a set, the number of elements it contains.

So we know what it means, how about you?

Cardinality 0 < Cardinality 1 < Cardinality 2 < Cardinality 0 < Cardinality ∞

Yes, I know that the cardinality of a set that has 1 member is less than the cardinality of a set that has 2 members, but that wasn't the question.

Examples are clearly given in http://www.internationalskeptics.com/forums/showpost.php?p=4972511&postcount=5578 and http://www.internationalskeptics.com/forums/showpost.php?p=4983714&postcount=5596 .

Once again, you either chose to not respond or purposly ignore things. I did not ask for examples, I asked for definitions. Post 5578 and 5596 does not even have the word "strong" in it.

And for Cardinality, you've changed it again, now it's

... (Cardinality) must be the measurement unit of any possible existence of some set including the existence of levels under some Complexity

Have you even defined Complexity?

 

[jsfisher]

...to quote Inigo Montoya, "You keep using that word. I do not think it means what you think it means."

• Wikipedia: In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
• Dictionary.com: (of a set) the cardinal number indicating the number of elements in the set.
• Wiktionary: (set theory) Of a set, the number of elements it contains.

So we know what it means, how about you?

Actually, it is worse than that for poor doron.

At the set theoretic level there are no numbers, and so the definition for cardinality doesn't involve numbers. Instead, you just start with |A| < |B| if and only if there is an injective mapping of the members of A to the members of B.

From there, you can develop the concept of equality, and then equivalence classes. Then you can select one member from each equivalence class (well, the finite ones, anyway) to represent the class (as is done in modular arithmetic). A convenient choice is the member from the von Neuman inductive set, which, in turn, conveniently translates into the integers.

By this point, doron's head would have asploded.

 

[doronshadmi]

The Man, please read this very carefully:


Cardinality is the measurement unit of the existence of things.


a) {} is a general notation of the atomic state.

b) The cardinality of the sub-existing things of {} is exactly 0.

c) This measurement is impossible without the existence of the atomic state, therefore the cardinality of the atomic state is greater than 0 and it is exactly the opposite of 0 and notated as ∞ (0 is the cardinality of non-existence, ∞ is the cardinality of total existence).

d) Things that their cardinality are ∞ or 0, do not enable Complexity.

e) Complexity is possible only if the cardinality of the existing thing is < ∞ and > 0.

f) Complexity is notated at least as "{{}}" and the cardinality of this complexity is exactly 1, such that 0 < 1 < ∞

g) By following (a) to (f) the cardinality of Complexity is x such that 0 < x < ∞.

Here are some examples of existing things that have cardinality x:

|{{}}|=1

|{{{}}}|=|{{},{}}|=1+1=2

|{{},{{}}}|=|{{{{}}}}|=1+1+1=3

|{{a,b,c,…}}| = |{N}| = |N| + 1

We immediately realize that Cardinality is the measurement unit of the existence of things, but it is not fine enough in order to distinguish between the details of Complexities.


This luck of sensitivity does not prevent from us to define the follows:

1) X is a set and any member of X (if exists) is a set.

2) If X is an infinite set, then |X| is a transfinite cardinal.

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

It is shown by jsfisher that (3) does not hold if Cardinality is a measurement that is limited only to the first level of sets.

But (3) holds if Cardinality measures the existence of complexities (in that case totalities like non-existence or total existence are ignored because they are not able the existence of Complexity, as shown in (c)).

In that case the Cardinality of X={{a,b,c,…}} = |{a,b,c,…}| + 1 and (3) holds.

 

[jsfisher]

The Man, please read this very carefully:


Cardinality is the measurement unit of the existence of things.

Doubly wrong. It is neither a unit nor a measure of existence.

Since the rest of the post builds on this absurd statement. There is no point considering the rest.

 

[The Man]

The Man, please read this very carefully:

Doron, please read this very carefully:

Cardinality is the measurement unit of the existence of things.

No it is the measure of the size of a set and you still have not explained exactly what “things” you think it is the measure of the “existence” of.

a) {} is a general notation of the atomic state.

No it is a pair of brackets that are often used to represent a set.

b) The cardinality of the sub-existing things of {} is exactly 0.

No that is the cardinality of the set “{}” itself and thus the size of the set, specifically the empty set.

c) This measurement is impossible without the existence of the atomic state, therefore the cardinality of the atomic state is greater than 0 and it is exactly the opposite of 0 and notated as ∞ (0 is the cardinality of non-existence, ∞ is the cardinality of total existence).

No the measurement is possible because of the definition of cardinality which has absolutely nothing to do with your imaginary “atomic state”. Again cardinality is a measure of the size of the set itself and thus a property of that set which is in this case (the empty set) is 0 not something “greater than 0”.


Before you were claiming “{}” the empty set as one of your “atomic states” now “the cardinality of the atomic state is greater than 0 and it is exactly the opposite of 0 and notated as ∞”. So now the ‘Doronality’ of the empty set is “∞” because “This measurement is impossible without the existence of the atomic state”?

d) Things that their cardinality are ∞ or 0, do not enable Complexity.

Well since you have yet to define your “complexity” this is a utterly meaningless as are most of the things you claim.

e) Complexity is possible only if the cardinality of the existing thing is < ∞ and > 0.

Well if those are the requirements for your “complexity” that you want to assert, but you will be held to them. Also it puts your “complexity” at a disadvantage as something of a non-finite cardinality has no “possible” complexity by your professed standard.

f) Complexity is notated at least as "{{}}" and the cardinality of this complexity is exactly 1, such that 0 < 1 < ∞

Wait cardinality was the “the measurement unit of the existence of things” by your first assertion, now it is “the cardinality of this complexity”. Which are you using it to measure your “complexity” or measure your “existence”. Perhaps as usual you just conflate the two?

g) By following (a) to (f) the cardinality of Complexity is x such that 0 < x < ∞.

So given up on “cardinality” of “existence” entirely now have you and it is just “cardinality of complexity"?

Here are some examples of existing things that have cardinality x:

So still ignoring the non-existing things that have “cardinality”, are you?

|{{}}|=1

|{{{}}}|=|{{},{}}|=1+1=2

|{{},{{}}}|=|{{{{}}}}|=1+1+1=3

|{{a,b,c,…}}| = |{N}| = |N| + 1

We immediately realize that Cardinality is the measurement unit of the existence of things, but it is not fine enough in order to distinguish between the details of Complexities.

Oh so now your back to “cardinality” of “existence” and giving up on “cardinality of complexity”?

This luck of sensitivity does not prevent from us to define the follows:

1) X is a set and any member of X (if exists) is a set.

2) If X is an infinite set, then |X| is a transfinite cardinal.

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

It is shown by jsfisher that (3) does not hold if Cardinality is a measurement that is limited only to the first level of sets.

But (3) holds if Cardinality measures the existence of complexities (in that case totalities like non-existence or total existence are ignored because they are not able the existence of Complexity, as shown in (c)).

In that case the Cardinality of X={{a,b,c,…}} = |{a,b,c,…}| + 1 and (3) holds.

Nope gone with the full conflation now I see as “Cardinality measures the existence of complexities” and throwing in your usual requirement of ignoring your own distinctions as “totalities like non-existence or total existence are ignored because they are not able the existence of Complexity”. Sorry Doron replacing the “existence of things” with the “existence of complexities” still does not answer the question.

So exactly what “things” is the value Z “a measurement unit of the existence of” other then simply the cardinality or size of set X depending on how the variable Y is used to demonstrate the lack of existence of irrational numbers in the set of positive integers?

Your above assertion in response to this question is basically ‘complex things’ with your claim that “Cardinality measures the existence of complexities”. So again you are simply asserting that cardinality is fundamentally a measure of, well, cardinality which is simply the size of a set. You can posit your “existence” or “complexity” on to that representation of the size of a set all you want, but your reasoning is simply self inconsistent as you claim in…

d) Things that their cardinality are ∞ or 0, do not enable Complexity.

As well as...

e) Complexity is possible only if the cardinality of the existing thing is < ∞ and > 0.

And….

f) Complexity is notated at least as "{{}}" and the cardinality of this complexity is exactly 1, such that 0 < 1 < ∞

And let’s not forget

g) By following (a) to (f) the cardinality of Complexity is x such that 0 < x < ∞.

But latter assert…

1) X is a set and any member of X (if exists) is a set.

2) If X is an infinite set, then |X| is a transfinite cardinal.

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

And…

But (3) holds if Cardinality measures the existence of complexities (in that case totalities like non-existence or total existence are ignored because they are not able the existence of Complexity, as shown in (c)).

In that case the Cardinality of X={{a,b,c,…}} = |{a,b,c,…}| + 1 and (3) holds.

Doron you specifically limited your ‘Doronality’ as what “measures the existence of complexities” to finite cardinalities. Remember you also claimed “in that case totalities like non-existence or total existence are ignored because they are not able the existence of Complexity, as shown in (c))”. By your own assertions your ‘Doronality’ of “the existence of complexities” does not apply to “a transfinite cardinal”. Again no one is likely to ever agree with you until you can at least show that you agree with yourself.

 

[doronshadmi]

No that is the cardinality of the set “{}” itself and thus the size of the set, specifically the empty set.

No, {} is an existing thing that has no sub-existing things, and this existing thing is called atom.

The cardinality of the non-existence of sub-things, is exactly 0.

The cardinality of the existence of {} is exactly ∞.

Standard Math uses cardinality in order to measure the things under cardinality ∞, by ignoring total existence, which is the opposite of non-existence (which its cardinality is 0).

It is obvious that non-existence (has cardinality 0) or total existence (has cardinality ∞) are the building-blocks that enable the rest of the existing things, such that their cardinality is > 0 and < ∞.

So the rest of the existing things is the result of the linkage between non-existence (has cardinality 0) and total existence (has cardinality ∞).

From this linked point of view any cardinality must be > 0 and < ∞. By focused on the results of the linkage, we are aware of the building-blocks that enable these results, in the first place, and by not ignoring these building-blocks each complex thing is an offspring of non-existence AND total-existence.

Furthermore, from this fundamental understanding we do not measure only the existence of the first-level of some complexity, as Standard Math does, and as a result Cardinality is generalized beyond this arbitrary limitation, and used to measure the complexity of any offspring.

The Man, you simply do not let your mind to understand things from their existence.

As a result you do not understand non-existence, total existence and no offspring of non-existence AND total-existence.

Moreover, you do not understand what a Set is, in the first place, and how non-existence AND total-existence is an extension of existence beyond totality.

As a result you do not understand Cardinality as the measurement unit of the existence of things, whether they are total (in the case of 0 or ∞) or not (in the case of x, such that 0 < x < ∞).

Standard Math is nothing but an arbitrary game with notations without notions, and as a result it can't deal with these simple facts:

1) X is a set and any member of X (if exists) is a set.

2) If X is an infinite set, then |X| is a transfinite cardinal.

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

It is shown by jsfisher that (3) does not hold if Cardinality is a measurement that is limited only to the first level of sets.

But (3) holds if Cardinality measures the existence of complexities (in that case totalities like non-existence or total existence are directly ignored because they are not able the existence of Complexity if they are not linked, but if linked they are used as the building-blocks of any measured offspring of them, where only an offspring is a complex existence).

In that case the Cardinality of X={{a,b,c,…}} = |{a,b,c,…}| + 1 and (3) holds.

Wait cardinality was the “the measurement unit of the existence of things” by your first assertion, now it is “the cardinality of this complexity”.

An offspring of non-existence AND total-existence (that cannot be but a complex thing) has cardinality x, such that 0 < x < ∞, so?

Please tell us The Man, what exactly prevents from you to understand total-existence as the opposite of non-existence?

Also please tell us why Cardinality is not the measurement unit of the existence of things, whether the measured is non-existence, total-existence or some of their offspring (which cannot be but a complex thing)?

 

[jsfisher]

No, {} is an existing thing that has no sub-existing things, and this existing thing is called atom.

Only in a fantasy world of make-believe, pretend Mathematics.

The cardinality of the non-existence of sub-things, is exactly 0.

Wrong.

The cardinality of the existence of {} is exactly ∞.

Wrong.

Standard Math uses cardinality in order to measure the things under cardinality ∞, by ignoring total existence, which is the opposite of non-existence (which its cardinality is 0).

Wrong.

...and so on.

 

[The Man]

<preceding nonsense sniped>

The Man, you simply do not let your mind to understand things from their existence.

If you mean that I do not simply purport fantasies as facts like you do, then you are correct.

I would ask you how you would define “existence”, but we all know what a waste of time that is and I doubt you have any consistent definition that, well, exists.

As a result you do not understand non-existence, total existence and no offspring of non-existence AND total-existence.

Moreover, you do not understand what a Set is, in the first place, and how non-existence AND total-existence is an extension of existence beyond totality.

Well as gibberish is not my native language you are going to have to translate those statements into something that gives at least the appearance of comprehensibility.

As a result you do not understand Cardinality as the measurement unit of the existence of things, whether they are total (in the case of 0 or ∞) or not (in the case of x, such that 0 < x < ∞).

Standard Math is nothing but an arbitrary game with notations without notions, and as a result it can't deal with these simple facts:

1) X is a set and any member of X (if exists) is a set.

2) If X is an infinite set, then |X| is a transfinite cardinal.

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

It is shown by jsfisher that (3) does not hold if Cardinality is a measurement that is limited only to the first level of sets.

But (3) holds if Cardinality measures the existence of complexities (in that case totalities like non-existence or total existence are directly ignored because they are not able the existence of Complexity if they are not linked, but if linked they are used as the building-blocks of any measured offspring of them, where only an offspring is a complex existence).

In that case the Cardinality of X={{a,b,c,…}} = |{a,b,c,…}| + 1 and (3) holds.


An offspring of non-existence AND total-existence (that cannot be but a complex thing) has cardinality x, such that 0 < x < ∞, so?

Well here you have simply reversed the order of your self inconsistency. This time first you claim your Doronality “measures the existence of complexities” and “(3) holds” referring to “a transfinite cardinal” then you again limit your “offspring of non-existence AND total-existence (that cannot be but a complex thing)” to finite cardinalities “x, such that 0 < x < ∞”.

Please tell us The Man, what exactly prevents from you to understand total-existence as the opposite of non-existence?

Existence of what? You still have not answered the question…

So exactly what “things” is the value Z “a measurement unit of the existence of” other then simply the cardinality or size of set X depending on how the variable Y is used to demonstrate the lack of existence of irrational numbers in the set of positive integers?

Again your recent posts tend to infer the “existence” you are referring to as the existence of your “complexity” yet you specifically limit that “complexity” to “cardinality x, such that 0 < x < ∞”. So your “total-existence” “∞” and “non-existence” “0” are not applicable to your notions of complexity or as you put it before “Things that their cardinality are ∞ or 0, do not enable Complexity”

“Please tell us” Doron “, what exactly prevents from you to understand” your own “total-existence”, “non-existence” and your specifically expressed limits which exclude both of those ascription of yours in your “complexity”?

Well it looks like the latest Doronophrase shift is being finalized, for those of you that remember the old favorites of ‘Local / Non-local Complementation’ or ‘Relation / Element Interaction’ it looks like ‘Existence / Non-existence Complexity’ might be the new dichotomist phrase.

Also please tell us why Cardinality is not the measurement unit of the existence of things, whether the measured is non-existence, total-existence or some of their offspring (which cannot be but a complex thing)?

What you mean other then the fact that it is the simply the size of a set as has already been explained to you time and time again. Doron that “Cardinality is” “the measurement unit of the existence of things” is your claim, it is up to you to support that claim in at least a self-consistent manor and apparently you can not. So it is you that clearly demonstrates “Cardinality is not the measurement unit of the existence of things” even by your own interpretations.

 

[doronshadmi]

Well here you have simply reversed the order of your self inconsistency. This time first you claim your Doronality “measures the existence of complexities” and “(3) holds” referring to “a transfinite cardinal” then you again limit your “offspring of non-existence AND total-existence (that cannot be but a complex thing)” to finite cardinalities “x, such that 0 < x < ∞”.

No, x is finite or transfinite cardinality, but you can't understand this fact because <preceding nonsense sniped> is your best "understanding" (you did not even try to get it, isn't it The Man?).

The rest of your reply is based on <preceding nonsense sniped> "understanding".

Since this is your basic attitude (you do not really wish to be opened to generalizations of agreed concepts) there is no use to dialog with you on this subject.

 

[zooterkin]

No, x is finite or transfinite cardinality, but you can't understand this fact because <preceding nonsense sniped> is your best "understanding" (you did not even tried to get it, isn't it The Man?).

The rest of your reply is based on <preceding nonsense sniped> "understanding".

Since this is your basic attitude (you do not really wish to be opened to generalizations of agreed concepts) there is no use to dialog with you on this subject.

Doron, you need to decide if you are creating your own alternative to mathematics, in which case you need to start from scratch, and define your terms rigorously, or if you want to use existing mathematics, in which case you need to understand and use the existing definitions of terms.

 

[doronshadmi]

Existence of what? You still have not answered the question…

One can't get abstract notions as follows:

1) He first needs to think about the absence of an existing X in order to get what non-existence is. In other words he does not have a direct understanding of non-existence, because he needs an absence of an existing X as a scaffolding to understand non-existence.

2) Exactly the same problem can be found when he tries to understand the opposite of non-existence, which is total existence. In this case he asks "Existence of what?" where his mind seeks after some existing X as a scaffolding to understand total-existence.

In other words, we can see here a parson that is unable to use direct perception in order to get abstract notions.

Please attribute quotes correctly.

Replying to this modbox in thread will be off topic  Posted By: LibraryLady

 

[ddt]

Having caught up with the last half dozen or so pages, I see that we're back at Doron not understanding cardinality and infinite sets.

How many times do we have to run in this same circle, Doron? When are you going to pick up a book, follow a course, whatever, but listen to those who know what they're talking about?

 

[The Man]

No, x is finite or transfinite cardinality, but you can't understand this fact because <preceding nonsense sniped> is your best "understanding" (you did not even try to get it, isn't it The Man?).

The rest of your reply is based on <preceding nonsense sniped> "understanding".


Since this is your basic attitude (you do not really wish to be opened to generalizations of agreed concepts) there is no use to dialog with you on this subject.

No problem, as you seem to some discrepancies to work out with yourself. Feel free to talk to yourself until you do work them out.

One can't get abstract notions as follows:

1) He first needs to think about the absence of an existing X in order to get what non-existence is. In other words he does not have a direct understanding of non-existence, because he needs an absence of an existing X as a scaffolding to understand non-existence.

2) Exactly the same problem can be found when he tries to understand the opposite of non-existence, which is total existence. In this case he asks "Existence of what?" where his mind seeks after some existing X as a scaffolding to understand total-existence.

In other words, we can see here a parson that is unable to use direct perception in order to get abstract notions.

Well that didn’t last very long, just 23 minutes and I didn't even need to make a post in that time.

1) He first claims “there is no use to dialog with you on this subject”; rather oblivious to the fact that he has never really engaged in a dialogue in the first place, just his own diatribe. In other words he does not have a direct understanding of what is being said to him or the standard math he constantly misrepresents because he needs that misrepresentation as a scaffolding to construct his fantasies.

2) Exactly the same problem can be found when he continues responding, but changes the name on the quote thinking that makes any difference. In this case as in the others it does not make any difference as he was never responding to what was being said but only to his own misinterpretations, where his mind seeks out something to misinterpret as a scaffolding to construct his total fantasies.


In other words we see here a person that is unable to conduct a dialogue with anyone other then himself, which is unfortunate since he can not seem to even agree with himself or hold to his own assertions (like not responding or not continuing what he considers to be a dialogue).

 

[doronshadmi]

<<preceding nonsense sniped> this is the best of closed minds that afraid of the show of themselves.


Look how yellow maneuvers they do in order to not get simple things like

|{{}}|=1

|{{{}}}|=|{{},{}}|=1+1=2

|{{},{{}}}|=|{{{{}}}}|=1+1+1=3

|{{a,b,c,…}}| = |{N}| = |N| + 1

and stay in their closed box where |{{a,b,c,…}}|=1


We do not need more than the absurd that {}, which is an existing thing, has cardinality 0.

So form one hand Cardinality is a measurement unit of what exists in some set, but on the other hand it ignores the existence of the set that actually enables things (or nothing) to be measured.

 

[The Man]

<<preceding nonsense sniped> this is the best of closed minds that afraid of the show of themselves.


Look how yellow maneuvers they do in order to not get simple things like

|{{}}|=1

|{{{}}}|=|{{},{}}|=1+1=2

|{{},{{}}}|=|{{{{}}}}|=1+1+1=3

|{{a,b,c,…}}| = |{N}| = |N| + 1

and stay in their closed box where |{{a,b,c,…}}|=1


We do not need more than the absurd that {}, which is an existing thing, has cardinality 0.

So form one hand Cardinality is a measurement unit of what exists in some set, but on the other hand it ignores the existence of the set that actually enables things (or nothing) to be measured.

Once again Doran you simply assert your own absurdity. The claim that “Cardinality is the measurement unit of the existence of things” is yours. That you simply can not seem to make up your mind what “things” you want to claim it is “the measurement unit of the existence of” is no ones problem but yours. Also the fact that you claim “Cardinality is the measurement unit of the existence of things” and “that {}, which is an existing thing, has cardinality 0” only demonstrates the absurdity of your claim about cardinality, so much so that you find the afore mentioned implication of your own claim to be absurd yourself.

 

[Little 10 Toes]

<<preceding nonsense sniped> this is the best of closed minds that afraid of the show of themselves.


Look how yellow maneuvers they do in order to not get simple things like

|{{}}|=1

|{{{}}}|=|{{},{}}|=1+1=2

|{{},{{}}}|=|{{{{}}}}|=1+1+1=3

|{{a,b,c,…}}| = |{N}| = |N| + 1

and stay in their closed box where |{{a,b,c,…}}|=1


We do not need more than the absurd that {}, which is an existing thing, has cardinality 0.

So form one hand Cardinality is a measurement unit of what exists in some set, but on the other hand it ignores the existence of the set that actually enables things (or nothing) to be measured.

Empty_set^WP: In mathematics, and more specifically set theory, the empty set is the unique set having no members; its size is zero.

Basically, cardinality doesn't care about the existance of a non-set nor of the non-existance of a set. It only cares about the number of members in a set. I will let those people who have greater knowledge than me to either confirm, deny, or correct me, my phrasing, and my understanding.

And what is/are "yellow maneuvers"? Why can't you understand simple things like the cardinality of the empty set?

 

[jsfisher]

3) If |X| is a transfinite cardinal, such that |X| > the cardinality of any member of X and any member of X is a finite set, then |X| is the smallest transfinite cardinal.

Doron, even with your complete misunderstanding of and criminal abuse to basic Mathematics, this conjecture of yours is still incorrect nonsense.

But let's put all that absurdity aside for one moment to give some prime time exposure to the real question:

What's it all good for?

Seriously, what is even just one practical application of doronetics? Neither Moshe nor you could come up with one before. Has anything surfaced since? Or is this just all one huge comprehension failure on your part that leads through a twisty path of contradiction, inconsistency, and gibberish?

Surely, that must be some practical purpose you can demonstrate, no?

 

[doronshadmi]

Once again Doran you simply assert your own absurdity. The claim that “Cardinality is the measurement unit of the existence of things” is yours. That you simply can not seem to make up your mind what “things” you want to claim it is “the measurement unit of the existence of” is no ones problem but yours. Also the fact that you claim “Cardinality is the measurement unit of the existence of things” and “that {}, which is an existing thing, has cardinality 0” only demonstrates the absurdity of your claim about cardinality, so much so that you find the afore mentioned implication of your own claim to be absurd yourself.

No The Man, it exposes the arbitrary limitations of Standard Math, which is a direct result of people like jsfisher and you.

Standard Math clearly measures the existence of what it calls "members of a set" where the measurement unite is called Cardinality.

In other words, Existence is inseparable of this measurement, but Standard Math arbitrarily limiting the measurement of existence in two ways:

1) It ignores the existence of the set that enables the measurement of the existence of members, in the first place.

2) Only the first level of the members is measured.

As a result Standard Math's framework can't deal (because of (1)) with total-existence (which its cardinality is exactly ∞) that is the exact opposite of nothingness (the cardinality of nothingness is exactly 0).

Also Standard Math's framework can't deal (because of (2)) with Complexity, which is the existence that its cardinality is x such that
0 < x < ∞, and this existence is the offspring of nothingness AND total-existence linkage.



This framework is based on arbitrary limitations:

|{{a,b,c,…}}|=|{{}}|=|{{{}}}|=|{{{{}}}}|= …= 1 and it can't deal with total-existence, and can't deal with Complexity.



This framework is natural:

|{{}}|= 0+1 = 1 < ∞

|{{{}}}|=|{{},{}}|= 0+1+1=0+1+0+1=2 < ∞

|{{},{{}}}|=|{{{{}}}}|=0+1+0+1+1=0+1+1+1=3 < ∞

|{{a,b,c,…}}| = |{N}| = |N| + 1 < ∞

…

 

[doronshadmi]

Surely, that must be some practical purpose you can demonstrate, no?

Yes, to take the Mathematical Science out of the hands of closed minds like The Man and you, which strangle this science to death by their arbitrary limitations, right at its foundations.

As a result this science becomes a blind force used by blind people, and the results of this blind force can be seen in any laboratory that uses this science in order to develop more and more "efficient" biological, chemical of atomic weapons, that have one and only one purpose, which is: Destroying Complexity.

Destroying Complexity is your expertise jsfisher, and you demonstrate it right from the foundations of your framework,
where |{{a,b,c,…}}|=|{{}}|=|{{{}}}|=|{{{{}}}}|= …= 1 .


Say no more.

 

[zooterkin]

Destroying Complexity is your expertise jsfisher, and you demonstrate it right from the foundations of your framework,
where |{{a,b,c,…}}|=|{{}}|=|{{{}}}|=|{{{{}}}}|= …= 1 .

Exactly why is that a problem?

If I'm counting packing cases, I'm interested in how many packing cases I have, not how many items there are in them.