Deeper than primes - Continuation

[doronshadmi]

What do you mean by 'power set'? A real power set, or a Doron 'power set'? If the latter, please supply clear instructions on what such a thing is, and how to create it.

If the former, then it should be trivial even for you to do (hint: look back at jsfisher's posts).

Please be aware that we are using elements that are constructed by 0;1 symbols.

For more details, please read vary carefully http://www.internationalskeptics.com/forums/showpost.php?p=8145045&postcount=948 , in order to understand better your restriction on the Diagonalization method (including Cantor's).

 

[zooterkin]

Please be aware that we are using elements that are constructed by 0;1 symbols.

For more details, please read vary carefully http://www.internationalskeptics.com/forums/showpost.php?p=8145045&postcount=948 , in order to understand better your restriction on the Diagonalization method (including Cantor's)).

How about actually answering the questions I asked?

I assume you mean your own special 'power set'. So, please, if you can, give a description of what it is, and how to construct them. Your 'examples' are not sufficiently rigorous to follow.

 

[doronshadmi]

So, the collection is complete, then?

Under your restrictions.

EDIT:

You simply ignored

In order to be able to construct an explicit element, which is not an element of a collection of 4 distinct elements of 0;1 symbols, the amount of symbols of each element of the given collection, must be at least the same as the amount of the elements of the given collection (only in this case Diagonalization can be used, and we can construct an explicit element, which is not an element of that collection).

in order to fit the reasoning into your restrictions.

 

[doronshadmi]

How about actually answering the questions I asked?

I assume you mean your own special 'power set'. So, please, if you can, give a description of what it is, and how to construct them. Your 'examples' are not sufficiently rigorous to follow.

How about being aware of your restrictions, which prevent the use of Diagonalization (including Cantor's)?

 

[zooterkin]

Under your restriction.

EDIT:

You simply ignored

in order to fit the reasoning into your restrictions.

How is it a restriction to allow the set to contain all its possible values?

 

[zooterkin]

How about being aware of your restrictions, which prevent the use of Diagonalization (including Cantor's)?

That does not in any way answer the questions I asked. Try again. If you can, give a description of what your 'power set' is, and how to construct one. Your 'examples' are not sufficiently rigorous to follow.

 

[doronshadmi]

How is it a restriction to allow the set to contain all its possible values?

What you call "all its possible values" is the result of your restriction on elements of 0;1 symbols, which prevent Diagonalization (including Cantor's).

 

[doronshadmi]

That does not in any way answer the questions I asked. Try again.

As long as you are not aware that your reasoning of "all its possible values" is the result of your restrictions, which prevent the use of Diagonalization (including Cantor's), you are unable to understand any of my answers.

Try again.

 

[doronshadmi]

Defined.

By using restrictions on Diagonalization (including Cantor's), so?

 

[jsfisher]

And all of this still distills down to the basic surprise Doron has to the fact a set of 4 elements does not have all the elements to be found in a set of 16.

Instead of finding this observation trivial (as all the rest of us do), Doron is convinced it is proof (without proof) that all sets are incomplete. This would be doron-incomplete, a concept Doron has not defined, and likely never will.

 

[jsfisher]

By using restrictions

Actually, zooterkin removed restrictions, artificial restrictions Doron had imposed.

Generalizing (the opposite of restricting) even more, in what sense is the set {1, 2, 3} doron-incomplete? What element is it missing that the set should have?

 

[doronshadmi]

Ok, zooterkin, let's see what we have and what we can get from it.

We are using collection of distinct elements that are constructed by 0;1 symbols (let's construct it from left to right):

S=
{
00,
10,
01,
11
}

We wish to construct its P(S), where |P(S)| = 2^4 = 16.

In order to get 16 distinct elements that are constructed by 0;1 symbols, we do the following:

S=
{
0000,
1000,
0100,
1100
}

so

S=
{
00,
10,
01,
11
}

is included in the elements that are constructed by 0;1 symbols, and now, we are able to construct

P(S)=
{
0000,
1000,
0100,
1100,
0010,
1010,
0110,
1110,
0001,
1001,
0101,
1101,
0011,
1011,
0111,
1111,
}

and we also realize that S version with 4 0;1 symbols for each distinct element, is incomplete, because there are explicit elements (found by using Diagonalization) with 4 0;1 symbols for each distinct element in P(S), which are not the elements of S version with 4 0;1 symbols for each distinct element.

 

[jsfisher]

Ok, zooterkin, let's see what we have and what we can get from it.

We are using collection of distinct elements that are constructed by 0;1 symbols (let's construct it from left to right):

S=
{
00,
10,
01,
11
}

We wish to construct its P(S), where |P(S)| = 2^4 = 16.

Why? The conjuncture was that no set was complete. Zooterkin offered this set, S = {00,01,10,11}. In what way is it incomplete? There is no need for this nonsensical aside about generating something that isn't a power set. You claim no set is complete. What's incomplete about S = {00,01,10,11} ?

 

[realpaladin]

Why? The conjuncture was that no set was complete. Zooterkin offered this set, S = {00,01,10,11}. In what way is it incomplete? There is no need for this nonsensical aside about generating something that isn't a power set. You claim no set is complete. What's incomplete about S = {00,01,10,11} ?

I have been paying attention... the correct answer in Dornetics is: "You don't get it!"

 

[laca]

Are we close to an epic series on "Why do people laugh at Doronetics"?

 

[doronshadmi]

S = {00,01,10,11} is considered as complete if we choose to restrict a collection of 4 distinct elements into two 0;1 symbols for each element.

So this, so called, completeness is simply the result of our restriction.

By not using this restriction, we are able two construct the powerset of the considered set, only if we are using at least 4 0;1 symbols for each element of the collection of 4 distinct elements.

By doing it, we are able to use Diagonalization, which explicitly provides us elements of the powerset, which have the same construction of the elements of the set, but they are not elements of the set.

In that case we conclude that the set is incomplete.

This conclusion holds, whether the amount of the distinct elements of the given set is finite or not.

Furthermore, since the largest powerset does not exist, this conclusion holds also for powersets, whether the amount of their elements is finite or not.

As long as, so called, mathematicians are not aware of the results of their decisions, they are not doing real Maths.

 

[jsfisher]

S = {00,01,10,11} is considered as complete if we choose to restrict a collection of 4 distinct elements into two 0;1 symbols for each element.

That is not a restriction. That is simply what the set is.

So this, so called, completeness is simply the result of our restriction.

So, the set is complete. Your initial assertion (that all sets were incomplete) is false.

No surprise there.

 

[doronshadmi]

Once again, as long as, so called, mathematicians are not aware of the results of their decisions (for example, they claim "That is simply what the set is") they are not doing real Maths, and this is one of my main augments all along this thread.

 

[jsfisher]

Once again, as long as, so called, mathematicians are not aware of the results of their decisions (for example, they claim "That is simply what the set is") they are not doing real Maths, and this is one of my main augments all along this thread.

So, Doron's view is that mathematicians don't do real math because they insist, for example, that if you define a set is a certain thing then that's what the set is.

How restrictive of these silly mathematicians, to actually require words and concepts have meaning.

 

[laca]

Once again, as long as, so called, mathematicians are not aware of the results of their decisions (for example, they claim "That is simply what the set is") they are not doing real Maths, and this is one of my main augments all along this thread.

Wow, doron. Just looking at what those morons (mathematicians not doing real Maths) have accomplished, I await with baited breath all that is still to come from you, Doron, the only one I know of that claims to be doing "real Maths"^TM.


















Oh wait, you've been doing it for how long? With no results whatsoever? Thanks, the world does not need your "real Maths". Why, you ask? Because it's just