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Deeper than primes

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jsfisher said:
Are you now saying it isn't indexed?
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Being indexed is not limited to N exactly becuse {},{1,2,3,...} and the subsets between {} and {1,2,3,...} are translatable to <0,1> forms.

In other words, we deal with P(N) members and not only with N members, but also in P(N) case the inverse of some diagonal of P(N) is not in the range of P(N), etc. ... ad infinitum ...

In other words, any collection that is translatable to <0,1> forms, is incomplete, whether it is N, P(N), P(P(N)), etc. ... ad infinitum ...
 
doronshadmi said:
Being indexed is not limited to N exactly becuse {},{1,2,3,...} and the subsets between {} and {1,2,3,...} are translatable to <0,1> forms.
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So, when you said my description of how you'd construct the diagonal was correct, what you actually meant was it wasn't? Can you describe any method of constructing the diagonal that doesn't involve natural numbers being used as indices?

The world awaits your revelation.
 
jsfisher said:
So, when you said my description of how you'd construct the diagonal was correct, what you actually meant was it wasn't? Can you describe any method of constructing the diagonal that doesn't involve natural numbers being used as indices?

The world awaits your revelation.
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EDIT:

Again. Being indexed is not limited to N, which is a fact that you can't comprehend, exactly because you can't comprehend that the subsets
of P(N) are also distinct indices, as clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=6820091&postcount=14141 .

Furthermore, by using the diagonal method on <0,1> forms it is shown that indices are incomplete, no matter if we deal with S, P(S), etc. ... ad infinitum ...

jsfisher your indices=natural numbers illusion prevents from you to get http://www.internationalskeptics.com/forums/showpost.php?p=6814651&postcount=14126 .
 
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doronshadmi said:
Your triangular form is a partial case of <0,1> form, for example:

1
11
111
1111
11111
...

and yet 00000..., which is the inverse of the diagonal of your triangular, is not in the range of the triangular, or in other words, the triangular form is incomplete.
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You mindlessly apply an argument that is not applicable to the case and that only supports the result of your brief diagnosis. (Yes, in this case DIAGonal and DIAGnosis are synonyms.) The diagonal method can be applied only with sets whose members have certain properties, but you apply it indiscriminately. But that's something that you can't comprehend.

If a ball is defined as B=1, then your reverse diagonal only refers to 5 objects that are not included, where one such an object is defined as C=0. So the set of balls is truly incomplete, and if C stands for Cockroach, then 5 cockroaches are missing from it.
 
doronshadmi said:
So what?

1.00000000
2.00000000
2.11111111
3.00000000
4.00000000
5.00000000
6.00000000
7.00000000

In that case 2.11011111 is not in the range, so?


Not at all

That means that any collection (finite or not) of distinct <0,1> forms is incomlete.
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The set

1.0000000
2.0000000
3.0000000
4.0000000
5.0000000
6.0000000
7.0000000
----------
Altered diagonal = 2.111111

was defined as having all members that are natural AND (logical connective) real numbers. Since 2.111111 is not a natural number, N AND R = False, and the set is missing a member that doesn't belong into it. Since you don't distinguish between naturals and reals, or have a great deal of difficulty to grasp the difference, you will never comprehend the example of the fallacy behind your "insightful" constructs.

Your molested diagonal argument says, among other things, that if a family of four is sitting in the living room at time t, the family set is incomplete and is missing other family members such as a goat, a squirrel, a bulldozer, Jupiter . . .
 
jsfisher said:
Go ahead, then. Describe how you'd construct the diagonal.

The world awaits your revelation, particularly the part where you have an index into a string of 0's and 1's that isn't a natural number.
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jsfisher,

1) Any given P(N) distinct member ( including {},(1,2,3,..) and any P(N) member between {} and {1,2,3,...} ) is translatable to <0,1> distinct form.

2) No P(N) member is an N member (even under the translation to <0,1> forms, a P(N) member is an infinite <0,1> distinct form, where a N member is a finite <0,1> distinct form exactly because the right infinitely long ...00000... of a given N member (where a mirror image of <0,1> forms is used), is ignored ).

3) The diagonal method is used on the P(N) members, and the P(N) member that is not in the range of P(N), is the inverse of such a diagonal.

4) No 1-to-1 mapping with N members is needed in order to explicitly define the P(N) member that is not in the range of P(N).

5) Since P(N) is incomplete, then if a 1-to-1 mapping is used between P(N) members and N members, it is discovered that also N is incomplete.

(1) to (4) are already shown in http://www.internationalskeptics.com/forums/showpost.php?p=6814651&postcount=14126.
 
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epix said:
You mindlessly apply an argument that is not applicable to the case and that only supports the result of your brief diagnosis. (Yes, in this case DIAGonal and DIAGnosis are synonyms.) The diagonal method can be applied only with sets whose members have certain properties, but you apply it indiscriminately. But that's something that you can't comprehend.

If a ball is defined as B=1, then your reverse diagonal only refers to 5 objects that are not included, where one such an object is defined as C=0. So the set of balls is truly incomplete, and if C stands for Cockroach, then 5 cockroaches are missing from it.
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If is not about balls (of any kind), it is about Distinction, and by using the diagonal method on you triangular form (when translated to <0,1> forms), it is explicitly shown an <0,1> form that is not in the range of this triangular form.

As long as you do not get Distinction as a general principle, you can't comprehend the diagonal method among <0,1> distinct forms.
 
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doronshadmi said:
...<gibberish>...
3) The diagonal method is used
...<igbberish>...
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Now, just that part right there. You need to explain that part without the usual linguistic throes or rapid arm movements you so commonly substitute for meaningful communication.
 
jsfisher said:
Now, just that part right there.
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A finger, which is a part of a given body, can't be understood by ignoring the body.

Since by your reasoning the body is ...<igbberish>... , then your reasoning actually determines the inability to understand the finger.
 
doronshadmi said:
A finger, which is a part of a given body, can't be understood by ignoring the body.

Since by your reasoning the body is ...<igbberish>... , then your reasoning actually determines the inability to understand the finger.
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Ok, so you cannot explain how to use the diagonal method. It was expected.
 
jsfisher said:
Ok, so you cannot explain how to use the diagonal method. It was expected.
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Wrong jsfisher.

Understanding X is essentially related to the ability to get also what is beyond X.

Your reasoning essentially ignores this simple fact.
 
doronshadmi said:
Wrong jsfisher.

Understanding X is essentially related to the ability to get also what is beyond X.

Your reasoning essentially ignores this simple fact.
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There is really only one simple fact, here: You don't understand the diagonal proof method.

You conceal your lack of understanding behind grandiose claims, but you are transparent and fooling no one except yourself. Your claims are bogus and contradictory; your conclusions are incompetent.

I would have thought any person of normal intelligence and reasoning ability would have recognized a problem when reaching an obviously incorrect result. Take for example the obviously incorrect result that there could be no 1-to-1 correspondence between the integers and even numbers. You didn't, though, Doron. Why is that?
 
doronshadmi said:
Wrong jsfisher.

Understanding X is essentially related to the ability to get also what is beyond X.

Your reasoning essentially ignores this simple fact.
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“what is beyond X” is specifically not part of “X” so “X” remains complete as “X” because it does not include “what is beyond X”.

Your preferred “fog” that you substitute for reasoning simply and deliberately ignores this fact in spite of your own assertion of “what is beyond X”.
 
doronshadmi said:
Wrong again,

Please see http://www.internationalskeptics.com/forums/showpost.php?p=6820757&postcount=14148 .
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It just confirms what I said:
Your molested diagonal argument says, among other things, that if a family of four is sitting in the living room at time t, the family set is incomplete and is missing other family members such as a goat, a squirrel, a bulldozer, Jupiter . . .
Click to expand...

It also again confirms that if someone can't comprehend an Euclidean common notion, then there is no way of explaining, coz common notions cannot be proven.

Here is once again your understanding of 1-on-1 correspondence used by Cantor to make conclusion about the cardinalities of countably infinite sets. You translated the set of naturals and evens into binary strings

natural: 1, 2, 3, 4, 5, 6, 7... => 1111111...
ev: 2, 4, 6, 8, 10, 12, 14 ... => 1010101...

and concluded that there can be no 1-on-1 correspondence between both classes, coz the binary string that represents evens happens to include zeroes. Such a conclusion is an indicator of a serious comprehension problem and there is no way of explaining due to . . . your serious comprehension problem. Right. That's why, when common notions are not understood, there is no way of deploying any arguments to correct the misunderstanding.
 
The Man said:
“what is beyond X” is specifically not part of “X” so “X” remains complete as “X” because it does not include “what is beyond X”.
Click to expand...

0001 what is beyond X is Y
0010 you can see it if you try
0011 there is other, looks like Z
0100 but that's something X can't see

;)
 
The Man said:
“what is beyond X” is specifically not part of “X”.
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Because X is a part of what is beyond it, and not vice versa.

EDIT:

The finger is a part of the body, but the body is not a part of the finger, and it is known exactly because one enables to get X AND beyond X simultaneously.
 
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jsfisher said:
There is really only one simple fact, here: You don't understand the diagonal proof method.
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The diagonal method is an axiom, jsfisher. Your limited mechanical reasoning simply can't comprehend http://www.internationalskeptics.com/forums/showpost.php?p=6820757&postcount=14148 .

jsfisher said:
Take for example the obviously incorrect result that there could be no 1-to-1 correspondence between the integers and even numbers. You didn't, though, Doron. Why is that?
Click to expand...

This is another example of your inability to get the <0,1> form, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6809590&postcount=14105 .
 
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