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Deeper than primes

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doronshadmi said:
F=
(
{
100,
110,
111
} → 000
or
{
101,
010,
000
} → 001
or

... etc. and we have at least 8 distinct F collections of 3 distinct objects each, where for each given F collection of 3 distinct objects we define a diagonal object that is not in the range of that F.

)

In other words, <0,1>^k(k=0 to ∞) is a general form for both P(F) and F, ... etc. ... ad infinitum ...
Click to expand...

The F set was defined as F = {apple, orange, lemon}. Now, the F set looks quite different -- its members are in the first case {100, 110, 111}

Those binary numbers are associated with P(F).
{
000 ↔ {}
001 ↔ {apple}
010 ↔ {orange}
011 ↔ {lemon}
100 ↔ {apple,orange}
101 ↔ {apple,lemon}
110 ↔ {orange,lemon}
111 ↔ {apple, orange, lemon}
}
Click to expand...
It follows that in the first case, the membership of set F is

F = {apple, {apple, orange}, {apple, orange, lemon}} = {{apple, {apple, orange}, F}.

The circular definition is pretty apparent. Are you going to fix it before explaining why F has a structure of the power set?
 
doronshadmi said:
P(S) is the power set of S, and no subsets are needed,
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The subsets of “S” are needed by the power set of “S” as its members (along with “S” and the empty set). That your “P(S)” does not include the subsets of “S” simply means it is not the power set of “S”.


doronshadmi said:
exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6771897&postcount=13944 ,
Click to expand...

That post shows nothing of the sort, it only shows that your “P(S)” is not the power set of “S”.

doronshadmi said:
such that the diagonal method demonstrates the incompleteness of any collection of non-empty distinct objects, and it is also equivalent to Godel's first incompleteness theorem.
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Nope.

doronshadmi said:
The Man, your reasoning does not hold water about this fine subject.
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You mean “this fine subject” where your “power set of S” isn’t the power set of “S”?
 
doronshadmi said:
The Man, your limited reasoning about P(S) as a collection of subsets of S, prevents from you to get the fact that the diagonal number (which is an object of P(S) ) is not in the range of any S, and the diagonal number (which is an object of P(P(S)) ) is not in the range of any P(S) etc... ad infinitum, whether S is finite or not.
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Doron your simple lack of reasoning "prevents from you to get the fact that the" power set of "S" specifically has all the subsets of "S" as members.

doronshadmi said:
You can't stop at some arbitrary S P(S) state and then conclude that P(S) is complete, exactly because P(S) is the set of P(P(S)), P(P(S)) is the set of P(P(P(S))) ...etc. ... ad infinitum ... and the <0,1>^k(k=0 to ∞) common form for both S and P(S) simply prevents such an arbitrary stop.
Click to expand...

Doron once again we conclude that all sets are complete since they have all and only the members they are defined to have. Once again you are simply and deliberately confusing the size of a set with the completeness of a set.

doronshadmi said:
Furthermore, your reasoning is based on the particular structure of subsets and can't comprehend the fact that this particular structure is nothing but the <0,1>^k(k=0 to ∞) form, which is itself a particular case of <0,1,3,...>^k(k=0 to ∞) that goes beyond P(S) S.
Click to expand...

No Doron my reasoning is based on the definition of what constitutes a member of some given set, which includes the definition of the members of the power set of some set.
 
jsfisher said:
Yeah, shame on you, The Man, for actually knowing what power set means. Weren't you paying attention? Doron has redefined power set and incompleteness and from there drawn all sorts of illogical conclusions.
Click to expand...

Oops, sorry, whatever was I thinking. Oh, wait that's the problem, I was thinking. I need to apply instead Doron’s "without any thoughts about it" reasoning.






















Wait for it…..























I think not.
 
Does anybody remember Doron addressing the issue with the two equivalent formalizations of the axiom of the empty set being different in his view? It's hard to keep track as he moves on to butcher other areas of Mathematics...
 
laca said:
Does anybody remember Doron addressing the issue with the two equivalent formalizations of the axiom of the empty set being different in his view? It's hard to keep track as he moves on to butcher other areas of Mathematics...
Click to expand...

Doron slides seamlessly from misunderstanding to misunderstanding without ever getting deep into anything.

Keep in mind this whole thread started with Doron discovering that multiplication was based on repeated addition. This triviality when applied to prime numbers led Doron absolutely nowhere, and he was content to explore it at some length.

And from those humble beginnings this epic thread follows, continuing the proud tradition of misunderstanding the defined, observing the trivial, confusing the known, while getting nowhere through the sheer power of illogic.
 
jsfisher said:
Doron slides seamlessly from misunderstanding to misunderstanding without ever getting deep into anything.

Keep in mind this whole thread started with Doron discovering that multiplication was based on repeated addition. This triviality when applied to prime numbers led Doron absolutely nowhere, and he was content to explore it at some length.

And from those humble beginnings this epic thread follows, continuing the proud tradition of misunderstanding the defined, observing the trivial, confusing the known, while getting nowhere through the sheer power of illogic.
Click to expand...

Sounds about right... :)
 
sympathic said:
You are lying. You consistently use the "I do not agree with this definition" approach, and then you try to redefine things. Only you can comment and disagree with things you do not understand. How convenient.
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I wrote "I agree with you" in this particular post, which you simply do not understand it.
 
The Man said:
The subsets of “S” are needed by the power set of “S” as its members (along with “S” and the empty set). That your “P(S)” does not include the subsets of “S” simply means it is not the power set of “S”.
Click to expand...
Wrong.

It simply means that you can't get the <0,1>^k(k=0 to ∞) general form for both S and P(S), so?
 
jsfisher said:
Doron slides seamlessly from misunderstanding to misunderstanding without ever getting deep into anything.
Click to expand...
Speak for yourself, because your collections-based relative-only reasoning is the exact reason of why you can't get the deep notion about the total (Emptiness, Fullness) and the relative (Collections between Emptiness and Fullness), as fundamentals of the mathematical science.
 
epix said:
Those binary numbers are associated with P(F).
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There is no association here.

The {x} {} form is translated to <0,1>^k(k=0 to ∞) general form for both S and P(S), such that {x} {} form is not considered anymore.
 
The Man said:
No Doron my reasoning is based on the definition of what constitutes a member of some given set, which includes the definition of the members of the power set of some set.
Click to expand...
Yes I knew, your reasoning is limited to {x},{} form for S P(S) and as a result you can't get deeper reasoning about S P(S), so?

Being proud about limited reasoning is not the best way for further deeper developments of some framework, and in this case the framework is the mathematical science, so?
 
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doronshadmi said:
There is no association here.

The {x} {} form is translated to <0,1>^k(k=0 to ∞) general form for both S and P(S), such that {x} {} form is not considered anymore.
Click to expand...
Aha. So the dictionary that helped to translate English text to Spanish is not considered anymore when Spanish is translated back to English. That's like if you translate 1 to 3 with the help of 2.

1 +2 = 3

When you translate back from 3 to 1, you don't need 2 anymore, coz the text translate itself automatically.

3 /3 = 1

I knew that you've been onto something special: self translating books! But you need to step on a bug called Slash, coz English to Spanish is to '+' as Spanish to English is to '-'.

Fortunately, no rules of logic govern over Doronetics, so there shouldn't be any problem.
 
epix said:
Aha. So the dictionary that helped to translate English text to Spanish is not considered anymore when Spanish is translated back to English. That's like if you translate 1 to 3 with the help of 2.

1 +2 = 3

When you translate back from 3 to 1, you don't need 2 anymore, coz the text translate itself automatically.

3 /3 = 1

I knew that you've been onto something special: self translating books! But you need to step on a bug called Slash, coz English to Spanish is to '+' as Spanish to English is to '-'.

Fortunately, no rules of logic govern over Doronetics, so there shouldn't be any problem.
Click to expand...
You still do not get it.

No 1-to-1 mapping (you call it association) is needed here, because both S and P(S) are based on the same <0,1>^k(k=0 to ∞) general form.
 
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