Deeper than primes

[doronshadmi]

It's all matter of definitions. Here is a 1-on-1 correspondence between Evens and Naturals.

2 - 4 - 6 - 8 - 10 - ...
1 - 2 - 3 - 4 - 5 - ...

You see that 2 and 4 are home sleeping, but at the same time they are outside the house looking through the window and do the counting.

Wrong epix, the "-on-" of your "1-on-1" does the counting and it is non-local w.r.t to the counted "1-";"-1".

EDIT:

In terms of Physics, the counter is http://en.wikipedia.org/wiki/Vacuum_state at the level of zero point field, which enables the finest observation of the counted. The Vacuum state is non-local observation w.r.t to any counted phenomena.

 

[epix]

Wrong epix, the "-on-" of your "1-on-1" does the counting and it is non-local w.r.t to the counted "1-";"-1".

"-on-" can count only one object. It's been quite a long time when something not an ape and not a human observed a flock of birds in the tree going

@ on
@@ on, on
@@@ on, on, on

and so... well, and so on.

Try to explain your insights into the process called "counting" to the anthropologist.

 

[doronshadmi]

"-on-" can count only one object. It's been quite a long time when something not an ape and not a human observed a flock of birds in the tree going

@ on
@@ on, on
@@@ on, on, on

and so... well, and so on.

Try to explain your insights into the process called "counting" to the anthropologist.

Wrong again.

For example:

By 1-on-2 "-on-" counts two things, "1" and "2".

In terms of Physics, the counter is http://en.wikipedia.org/wiki/Vacuum_state at the level of zero point field, which enables the finest observation of the counted. The Vacuum state is non-local observation w.r.t to any counted phenomena because any phenomena is born from the zero point field.

 

[epix]

Wrong again.

For example:

By 1-on-2 "-on-" counts two things, "1" and "2".

In terms of Physics, the counter is http://en.wikipedia.org/wiki/Vacuum_state at the level of zero point field, which enables the finest observation of the counted. The Vacuum state is non-local observation w.r.t to any counted phenomena because any phenomena is born from the zero point field.

Yes, "double U" = W is 1 letter and "double U" = UU are 2 letters.

1) As I said before, it's all matter of definitions.
2) As I said before, Ignorance is our Salvation


1 on 2 and 3 on 4
5 on 6 and there is more
6 on 7, 8 on 9
learn to count and you'll be fine

numbers sometimes show in pairs
learn to count or climb the stairs
down is sooner, up is later
you better use the elevator

 

[zooterkin]

As can be seen P(S) is represented by the binary "silly notation":

• { } = 000
• {x} = 100
• {y} = 010
• {z} = 001
• {x, y} = 110
• {x, z} = 101
• {y, z} = 011
• {x, y, z} = 111

where S is some collection of 3 distinct binary "silly notations" out of
P(S) collection of 8 distinct binary "silly notations".

Yes, but that representation actually works, unlike your examples. If you look closely, it's a bitmap of the elements present. Perhaps you could redo your example to conform.

 

[jsfisher]

Whoop-de-do!! There is a diagonal form of this "silly notation" which actually proves that a collection of distinct subsets of S (known as the powerset of S) is incomplete

No, it shows that the silly notation doesn't work for expressing the full membership of the power set. Why are you unable to comprehend this obvious fact. The diagonal method provides a very simple proof by contradiction that the silly notation falls apart with infinite sets. The notation could be said to be incomplete, but it shows nothing about the power set.

 

[jsfisher]

Here is a good example taken from http://en.wikipedia.org/wiki/Power_set , which follows jsfisher's argument.

As can be seen P(S) is represented by the binary "silly notation":

• { } = 000
• {x} = 100
• {y} = 010
• {z} = 001
• {x, y} = 110
• {x, z} = 101
• {y, z} = 011
• {x, y, z} = 111

where S is some collection of 3 distinct binary "silly notations" out of
P(S) collection of 8 distinct binary "silly notations".

Oh, Doron, you were doing so well up until that last part. The set S is {x,y,z} in this example. In the silly notation that would be 111, not the nonsense you put at the end.

You keep insisting on changing S when you get near the finish. If S is one thing at the beginning then something entirely different at the end, then you've done something wrong.

 

[epix]

Yes, but that representation actually works, unlike your examples. If you look closely, it's a bitmap of the elements present. Perhaps you could redo your example to conform.

Doron doesn't have the slightest idea what the classic Cantorian power set was good for. So he is not aware of the fact that distinct x, y, and z are not natural numbers, or the counting numbers, and so some other method has to show that all subsets of an infinite set whose members are not counting numbers or are uncountably infinite. Since there is infinitude of natural numbers, then there can't be an infinitude of anything you can imagine that the naturals couldn't be in correspondence with. But that's like a optical effect that can fool you. Under the right definitions, you can play trick with the idea that naturals are infinite -- you can trick-delete the ellipses from 1, 2, 3, . . .

 

[doronshadmi]

Oh, Doron, you were doing so well up until that last part. The set S is {x,y,z} in this example. In the silly notation that would be 111, not the nonsense you put at the end.

You keep insisting on changing S when you get near the finish. If S is one thing at the beginning then something entirely different at the end, then you've done something wrong.

In the case of infinite collection we get a 1-to-1 beween the "silly notation" and the members of P(S) as follows:

000... ↔ { }
100... ↔ {x}
010... ↔ {y}
001... ↔ {z}
110... ↔ {x,y}
101... ↔ {x,z}
011... ↔ {y,z}
...

and yet there is a diagonal "silly notation" that is not the range of P(S), so P(S) is incomplete.

 

[zooterkin]

In the case of infinite collection we get a 1-to-1 beween the "silly notation" and the members of P(S) as follows:

000... ↔ { }
100... ↔ {x}
010... ↔ {y}
001... ↔ {z}
110... ↔ {x,y}
101... ↔ {x,z}
011... ↔ {y,z}
...

and yet there is a diagonal "silly notation" that is not the range of P(S), so P(S) is incomplete.

Where?

 

[jsfisher]

In the case of infinite collection we get a 1-to-1 beween the "silly notation" and the members of P(S) as follows:

000... ↔ { }
100... ↔ {x}
010... ↔ {y}
001... ↔ {z}
110... ↔ {x,y}
101... ↔ {x,z}
011... ↔ {y,z}
...

and yet there is a diagonal "silly notation" that is not the range of P(S), so P(S) is incomplete.

There is an integer "not in the range of" {1,2,3}. So what! The set {1,2,3} is complete. It has all of the members it is supposed to have, omitting none of them.

Sets don't have members they are not supposed to have. That doesn't make them incomplete. It makes them useful. Now, admittedly there is nothing in Doronetics that pretends to be useful, so maybe it doesn't matter there, but in real Mathematics, utility is often desirable.



(And, by the way, this set P(S) you are keep trying to redefine isn't the power set of S.)

 

[doronshadmi]

There is an integer "not in the range of" {1,2,3}. So what! The set {1,2,3} is complete.

EDIT:

No, it is incomplete, whether it is finite or infinite collection, for example, this is P(S) infinite collection:

000... ↔ { }
110... ↔ {x,y}
100... ↔ {x}
101... ↔ {x,z}
010... ↔ {y}
011... ↔ {y,z}
001... ↔ {z}
...

where the diagonal's first 3 symbols, in this case, is 101...

and this incompleteness is exactly the ability of a given thing to be developed beyond its current state, which is the essence of usefulness.

(And, by the way, this set P(S) you are keep trying to redefine isn't the power set of S.)

Yes, it is infinite P(S), and it is incomplete, as demonstrated above.

Usefulness is not less than Whole\Parts Relations where the Whole is beyond the limitations of the parts, which enables the development of each part beyond its current partial case.

Your mechanical reasoning, which according to it the Whole is the sum of its parts, is an obsolete reasoning, which has no ability to deal with real complexity, as demonstrated among living creatures.

Organic Mathematics is the further development beyond your mechanical reasoning, where concepts like Emptiness, Fullness, Non-locality (in addition to Locality, which is the only thing that your mechanical reasoning deals with) and the new understanding of the concept of Collection as an open and ever developing realm w.r.t the totality of Emptiness (that has not predecessor) and Fullness (that has no successor).

Furthermore your mechanical reasoning has no ability to comprehend the naturally undefined, which if defined, is the source of defined concepts like Emptiness, Fullness, Collection, Locality and Non-locality.

Sets don't have members they are not supposed to have. That doesn't make them incomplete. It makes them useful.

In other words jsfisher, you have no clue how non-usful is your mechanical reasoning for the future of the mathematical science.

In terms of Physics, the counter is http://en.wikipedia.org/wiki/Vacuum_state at the level of zero point field, which enables the finest observation of the counted. The Vacuum state is non-local observation w.r.t to any counted phenomena because any phenomena is born from the zero point field.

Your mechanical reasoning can't get the zero point field ( known also as the unified field http://www.internationalskeptics.com/forums/showpost.php?p=6732750&postcount=13826 ).

 

[doronshadmi]

Where?

EDIT:

000... ↔ { }
110... ↔ {x,y}
100... ↔ {x}
101... ↔ {x,z}
010... ↔ {y}
011... ↔ {y,z}
001... ↔ {z}
...

where the diagonal's first 3 symbols, in this case, is 101...

 

[doronshadmi]

Doron doesn't have the slightest idea what the classic Cantorian power set was good for.

The Cantorian set as a complete mathematical object is an illusion, at the moment that you are able to understand Emptiness, Fullness, Non-locality and the new understanding of the concept of Collection as an open and ever developing realm w.r.t the totality of Emptiness (that has not predecessor) and Fullness (that has no successor).

 

[doronshadmi]

You keep insisting on changing S when you get near the finish. If S is one thing at the beginning then something entirely different at the end, then you've done something wrong.

jsfisher you keep insisting not to get the generalization of <0,1>^k (k = 1 to ∞) form in http://www.internationalskeptics.com/forums/showpost.php?p=6791520&postcount=13995

 

[zooterkin]

EDIT:

000... ↔ { }
110... ↔ {x,y}
100... ↔ {x}
101... ↔ {x,z}
010... ↔ {y}
011... ↔ {y,z}
001... ↔ {z}
...

where the diagonal's first 3 symbols, in this case, is 101...

So much wrong, where to begin...

First of all, in the list, the bolded numbers are 010, yet for some reason you say the diagonal is 101. Explain.

Second, why have you not listed all the possibilities? If you don't do that, then obviously there will be some missing (and you, equally obviously, have not listed the power set).

Third, why have you added '...' to all the possibilities? What is that supposed to mean?

ETA: Fourth, you pick out '101' as your number, but that is in the list. In what way is it missing?

 

[jsfisher]

...and this incompleteness is exactly the ability of a given thing to be developed beyond its current state, which is the essence of usefulness.

Just how does that make it incomplete? You keep offering an element not in a set as proof the set is incomplete. That isn't what incomplete means. You really, really should have asked for good dictionary for Hanukkah instead of those socks.

Yes, it is infinite P(S), and it is incomplete, as demonstrated above.

(1) You have never demonstrated that your set P(S) is the power set of S, and since it isn't you will be hard-pressed to proof it is, but I welcome you to try.

(2) You have never demonstrated that your set P(S) is incomplete, either. All you continually do is point out elements that aren't in the set. Many things aren't in the set. Why do you find this so surprising?

 

[doronshadmi]

Just how does that make it incomplete? You keep offering an element not in a set as proof the set is incomplete. That isn't what incomplete means. You really, really should have asked for good dictionary for Hanukkah instead of those socks.

Incompleteness, in this case, is the ability to show that some collection is a part of a bigger collection.

The bigger collection in the case of {1,2,3} is {1,2,3,...}, but also {1,2,3,...} is a part of the powerset of {1,2,3,...}, etc. ... ad infinitum (and again, the set of all powersets does not exist).

You really really have to do some paradigm-shift in your mind about completeness, because only Emptiness and Fullness are complete, where the intermediate existence between these totalities is incomplete exactly because it is above Emptiness and below Fullness.

(1) You have never demonstrated that your set P(S) is the power set of S, and since it isn't you will be hard-pressed to proof it is, but I welcome you to try.

Wrong.
{
0000000... ↔ { },
1100000... ↔ {x,y},
1000000... ↔ {x},
1010000... ↔ {x,z},
0100000... ↔ {y},
0110000... ↔ {y,z},
0010000... ↔ {z},
...
}
is the powerset of {x,y,z,...} (where there are infinitely many distinct symbols like "x","y" or "z" for example: "@", "%" , "&", "*", etc... ad infinitum), and the diagonal that is not in the range of P(S) starts by 1011111..., in this case.

(2) You have never demonstrated that your set P(S) is incomplete, either. All you continually do is point out elements that aren't in the set. Many things aren't in the set. Why do you find this so surprising?

1011111... is exactly an element that has the same form of the elements in the set, but it is not in the range of that set, or in other words, the given set is incomplete because I show exactly what element is not in its range.

Please do not use constructivist approach and ask me to draw all the elements of a given infinite collection, in order to prove my diagonal argument about the incompleteness of

{
0000000... ↔ { },
1100000... ↔ {x,y},
1000000... ↔ {x},
1010000... ↔ {x,z},
0100000... ↔ {y},
0110000... ↔ {y,z},
0010000... ↔ {z},
...
}

 

[doronshadmi]

So much wrong, where to begin...

First of all, in the list, the bolded numbers are 010, yet for some reason you say the diagonal is 101. Explain.

Second, why have you not listed all the possibilities? If you don't do that, then obviously there will be some missing (and you, equally obviously, have not listed the power set).

Third, why have you added '...' to all the possibilities? What is that supposed to mean?

ETA: Fourth, you pick out '101' as your number, but that is in the list. In what way is it missing?

Please read http://en.wikipedia.org/wiki/Cantor's_diagonal_argument in order to understand the diagonal argument.

After you get it, then please read http://www.internationalskeptics.com/forums/showpost.php?p=6797042&postcount=14018 .

 

[doronshadmi]

About ZPE (Zero Point Energy) please start by http://video.google.com/videoplay?docid=-5738531568036565057# ( Free Energy - Zero-Point Energy Extraction from the Quantum Vacuum by Tom Valone )