Deeper than primes

[Little 10 Toes]

The cardinality of the members of the empty set is 0.

The cardinality of Set (whether it is empty or not) is the cardinality of total-existence (notated as ∞).

The cardinality of finite or infinite members < ∞

Cardinality applies to a set, not the members of the set. The rest of your flawed ideas are based on the flawed understanding.

Set does not have cardinality.^* However a set does have cardinality. A non-existent set has no cardinality while a set that is empty will have a cardinality of zero.


^*Hey, doronshadmi capitalized it, and due to his past history, I figured it was this Set he was talking about.

 

[ddt]

Cardinality applies to a set, not the members of the set. The rest of your flawed ideas are based on the flawed understanding.

Set does not have cardinality.^* However a set does have cardinality. A non-existent set has no cardinality while a set that is empty will have a cardinality of zero.

^*Hey, doronshadmi capitalized it, and due to his past history, I figured it was this Set he was talking about.

I thought doron was referring to the category of all sets. As cardinality is not defined on categories, it is nonsense. Even when I'm nice and apply it to its collection of objects, it doesn't fit, as that collection doesn't fit within ZFC.

 

[The Man]

So many words but no understanding of the cardinality of total-existence (notated as ∞), isn't it The Man?

Please show Cardinality ∞ as a part of Standard Math.

There is no problem for you to ignore:


isn't it The Man?

Following the tradition of your ignorance we can add http://www.internationalskeptics.com/forums/showpost.php?p=4992070&postcount=5627 too to your body of "knowledge".

Once again Doron the claim that “Cardinality is the measurement unit of the existence of things” is yours. Any problems that results from your ascription as such are also simply yours. That you simply ignore your own problems and try to ascribe them to others is your demonstrative “tradition”. Break your tradition Doron of ignoring that you simply create problems for yourself then just disagree with yourself about your solutions or the source of your problems.

Please define the set of “total-existence” so that we can examine its cardinality. So far your only representation of this set has been “{” “}”, which is simply not a set. One way to define a set is by defining what constitutes a member of that set. If you are going to make that definition as anything that exists then the set itself would be a member of itself and we are back to the discussion of proper classes of sets as ddt alludes to above. You have gone a long way around Doron, seemingly just to end up where these discussions of your notions were a year or two ago.

 

[doronshadmi]

First of all, HAPPY BIRTHDAY TO YOU jsfisher

So you might think, but we don't make stuff up as a substitute for things we don't understand.

We also don't claim the idiocy |{}| = ∞.

No, |{}| = 0 , where 0 is the cardinality of the existence of the members of {}.

The cardinality of the existence of Set (notated by the outer "{" "}") whether it is empty or not, is exactly ∞ and it is greater than the cardinality of any collection of members.

Set's existence is equivalent to an existing stage that exits independently of the existence of players on it.

We also don't claim the idiocy 2 is not a member of {2, 3}.

2 and {2} is not the same thing when Complexity is not ignored (as it is ignored by Standard Math), so?

We also don't claim the idiocy 0 is a positive number.

I do not claim this too, so?

We also don't claim the idiocy 0 = 1/3 = 1/4 = 2/3 = 1.

I do not claim this too (these are simply local numbers), so?

We also don't claim the idiocy set membership is indeterminate.

Non-locality is not fully captured by any given domain, so?

We also don't claim the idiocy sets, maps, and functions are the same thing.

Because you do not get Non-locality and the cardinality of Non-locality, which is exactly ∞, so?

We also don't claim the idiocy 1/4 and 0.25 are different numbers.

Because your framework can't deal with Non-locality and can't deal with Complexity, so?

We also don't claim the idiocy there are fewer than 1 real numbers.

I do not claim this too, so?

We also don't claim the idiocy |Q| = |R|.

I do not claim this too if the internal strucure of each member of Q or R sets is not ignored (and it cannot be ignored even if we play jsfisher's { {{}}, {{a}}, {{a,b}}, ... , {{a,b,c,...}}, ... } limited game) so?

We also don't claim the idiocy X really means X=X.

X alone is not a researchable framework, so?

We also don't claim the idiocy if A<C then you cannot have A<B<C.

Ho yes you do, by claiming that A as an immediate predecessor of C.

It is a fact jsfisher that your club's diploma does not help you to understand a single word of what I say ( for example: http://www.internationalskeptics.com/forums/showpost.php?p=4992270&postcount=5628 ).

Your club's body of knowledge is trivial and misleading, exactly as I show in http://www.internationalskeptics.com/forums/showpost.php?p=4989523&postcount=5619 .

 

[doronshadmi]

One way to define a set is by defining what constitutes a member of that set.

Nonsense.

Set is equivalent to a stage which exists independently of the existence of the players on it.

Existence is the fundamental principle of Cardinality, and Standard Math uses a limited version of Existence, which is focused only on the first level of existence of possible players on this stage, which its cardinality is exactly is ∞.

It is ok as long as we are aware of the fact that we are using a limited version of Existence.

The problem with Standard Math is that it determines a limited case of X as if it is a general case of X.

Say no more.

If you are going to make that definition as anything that exists then the set itself would be a member of itself and we are back to the discussion of proper classes of sets as ddt alludes to above.

Since you do not understand Non-locality (which its Cardinality is exactly ∞) you force on it your local only point of view, and as a result you do not understand that membership (non-locality) cannot be a member (locality) and vise versa.

Look at this:

The outer "{" "}" is membership.

Anything under membership is a member but membership is Non-local w.r.t any given member.

As set that it is its own member has, for example, this structure:

{ …{{{…{} …}}}…} and as you see membership is beyond the non-finite interpolation\extrapolation of members.

 

[doronshadmi]

I thought doron was referring to the category of all sets. As cardinality is not defined on categories, it is nonsense. Even when I'm nice and apply it to its collection of objects, it doesn't fit, as that collection doesn't fit within ZFC.

No, I refer to Non-locality, which its existence it greater than any collection, whether it is called Set, Category, Proper Class, or any other name that is given to Collections.

 

[doronshadmi]

Cardinality applies to a set, not the members of the set.

Cardinality applies to Existence.

 

[zooterkin]

Cardinality applies to Existence.

Choose your own words if you want to define a new concept.

 

[doronshadmi]

Choose your own words if you want to define a new concept.

No I do not.

Cardinality is the measurement of the existence of things.

Standard Math uses this measurement only for the first level of members.

I do not use these arbitrary limitations, simple as that.

 

[sympathic]

No I do not.

Cardinality is the measurement of the existence of things.

Standard Math uses this measurement only for the first level of members.

I do not use these arbitrary limitations, simple as that.

How very convenient of you. I don't like the fact that the skies are blue. From now on they are red. Simple as that.

 

[Little 10 Toes]

Cardinality applies to Existence.

Define Existence (capital e).

 

[ddt]

No, I refer to Non-locality, which its existence it greater than any collection, whether it is called Set, Category, Proper Class, or any other name that is given to Collections.

What is non-locality? Never mind, we've been over this for more than a year. Thus far, you failed to give any definition at all.

And happy birthyday, jsfisher!

 

[sympathic]

Nonsense.

Set is equivalent to a stage which exists independently of the existence of the players on it.

This is the root of your misunderstanding.

Set is a concept. Much like Classes in object oriented programming (you gave some examples from Lisp, so maybe you can relate to this...). Objects or instances are different than Classes. You can perform operations on instances but not on classes. For example to get the size of a set (cardinality) you need to refer to an actual set (object) - the empty set is a set, {1} is a set, etc. You can not apply size on the concept of a Set.

 

[Apathia]

Still lurking, holding my tongue, and slapping my hand that wants to type out that quotation of Humpty Dumpty in Through The Looking Glass,

Have a happy B-Day Fisher.

 

[doronshadmi]

You can not apply size on the concept of a Set.

Yes I can if the measurement unit refers to the existence of the measured thing, and this is exactly what Cardinality is.

In the case of Standard Math this measurement of existence is arbitrarily limited to the first level of existence of the measured members of Set.

And it is arbitrarily limited exactly because Standard Math take this partial case as if its is the general case of Cardinality.

 

[jsfisher]

Still lurking, holding my tongue, and slapping my hand that wants to type out that quotation of Humpty Dumpty in Through The Looking Glass

But it is such a very applicable quotation.

Have a happy B-Day Fisher.

Thanks!

 

[doronshadmi]

How very convenient of you. I don't like the fact that the skies are blue. From now on they are red. Simple as that.

This is a fact exactly as arbitrary limitation is a fact, so?

 

[doronshadmi]

What is non-locality?

Memebership, for example.

 

[doronshadmi]

Define Existence (capital e).

That is not nothingness.

 

[The Man]

Yes I can if the measurement unit refers to the existence of the measured thing, and this is exactly what Cardinality is.

Well it isn’t, it doesn’t, so you can’t. That is why even you call the implications of your own application are absurd. Doron, be our guest and continue to hold a perspective you claim is absurd yourself.






And of course

Happy Birthday JS.