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Deeper than primes

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Originally Posted by epix
Mammals exist in two categories: the male and the female category.
11589_port_man_woman_520.jpg


According to your version of the diagonal argument,
http://www.internationalskeptics.com/forums/showpost.php?p=6808846&postcount=14088
the two categories are not complete. Which category is missing?



doronshadmi said:
Where is the child?
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The child? What do you need to see the child for? Just take my word for it: children are divided into two categories -- male and female -- as well. There is no additional missing category no matter what your diagonal argument tells you. But if you don't believe me, here is the proof:

1) mammals = male XOR female
2) IF mammals = humans AND humans = children, THEN mammals = children
3) conclusion: children = male XOR female
 
jsfisher said:
OMG!!! Arithmetic has suddenly stopped working. The natural correspondence between the natural numbers and the positive even numbers (i.e. f(i) = 2i) is now broken.
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Nothing was broken, by using <0,1> form, the set of natural numbers has a diferent code than any proper subset of it, exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6808937&postcount=14090 .

As about magnitude, if it is determined by the number of bit 1 w.r.t <0,1> form of a given code, then the set of natural numbers has greater magnitude than any proper subset of it.
 
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doronshadmi said:
Yes, the offspring, which is male or female, but he\she is not identical to his\her parents.
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There are two distinct categories: 1) male, 2) female. Your version of the diagonal argument tells you that there must be at least one more category, that is category #3. What is the category? The domain is gender, and not any broader genetic inheritence issue that you try to sneak in to cover up your nonsense.

What is the 3rd category, Doron? The missing apple from here?
http://www.internationalskeptics.com/forums/showpost.php?p=6809217&postcount=14098
 
epix said:
There are two distinct categories: 1) male, 2) female. Your version of the diagonal argument tells you that there must be at least one more category, that is category #3. What is the category? The domain is gender, and not any broader genetic inheritence issue that you try to sneak in to cover up your nonsense.

What is the 3rd category, Doron? The missing apple from here?
http://www.internationalskeptics.com/forums/showpost.php?p=6809217&postcount=14098
Click to expand...

You still miss it.

The complement of the diagonal of the <0,1> forms is also an <0,1> form, which is not in the range of the collection of the <0,1> forms, exactly because it has a <0,1> code that is different than any <0,1> form of the given collection, whether this collection of distinct <0,1> forms is finite or not (or whether it is powerset or not).

The collection is incomplete exactly because there is an object that is based on the same principle but it is not in the range of the collection of objects, which share with it this principle.
 
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doronshadmi said:
Meaning you can't get a self evident truth. How not surprising.
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The self truth of an axiom you cannot even express? Get real, Doron. We are not mind readers, here.

If you think there must be an axiom having something to do with the diagonal method, then, please, express it. Otherwise, we will rightfully again conclude you are just making things up to cover for a total lack of understanding.

No correspondence between nature numbers and the positive even integers? What color is the sky in your world, Doron?
 
doronshadmi said:
You still miss it.

The complement of the diagonal of the <0,1> forms is also an <0,1> form, which is not in the range of the collections of the <0,1> forms, exactly because it has a <0,1> code that is different than any <0,1> form of the given collection, whether this collection of distinct <0,1> forms is finite or not (or whether it is powerset or not).
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I don't miss anything. You explained the consequence of the above pretty clearly:
No epix, the diagonal argument is exactly a proof that any collection of finite or infinite distinct objects (whether the collection is powerset or not) is incomplete, because by using it one explicitly defines an object that has the same form of the distinct objects of a given collection, but it is not in the range of the given collection.
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The are two gender categories in the class Mammalia: male and female. According to your discovery, the gender categoris are not complete. What is the 3rd category?
 
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epix said:
I don't miss anything. You explained the consequence of the above pretty clearly:

The are two gender categories in the class Mammalia: male and female. According to your discovery, the gender categoris are not complete. What is the 3rd category?
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The collection is incomplete exactly because there is an object that is based on the same principle but it is not in the range of the collection of objects, which share with it this principle, because it is different than any object of that collection.
 
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jsfisher said:
The self truth of an axiom you cannot even express? Get real, Doron. We are not mind readers, here.
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You don't have too.

The diagonal method works on any collection of distinct objects (finite or not, powersets or not), and it is a self evident truth without any need of extra words.

All is needed is to look at it and see how it works on any collection of distinct objects, exactly as demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=6808813&postcount=14086 .
 
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doronshadmi said:
You don't have too.
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You are correct. I do not have to. It wasn't my brain fart; it was yours, and you are the one who should express what you mean by it. You are completely unable to do so, though.

The diagonal method works on any collection of distinct objects (finite or not, powersets or not), and it is a self evident truth without any need of extra words.
Click to expand...

No it doesn't, and no it isn't. You would have to be self-delusional to believe that.
 
doronshadmi said:
The collection is incomplete exactly because there is an object that is based on the same principle but is not in the range of the collection of objects, which share with it this principle, because it is different than any object of that collection.
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Now you are talking. The third gender category could be called "The Pink Chicken of Perpetual Motion."

For kristsake, Doron, that question wasn't so difficult to answer. Cantor couldn't put some real numbers into 1-to-1 correspondence with the counting numbers, but didn't identify those particular real numbers either. What matters is that the object simply isn't there. Here read this:
The purpose of set theory is not practical application in the same way that, for example, Fourier analysis has practical applications. To most mathematicians (i.e. those who are not themselves set theorists), the value of set theory is not in any particular theorem but in the language it gives us.
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The set theory is completely and utterly disconnected from the way nature works, and so the male/female incomplete category doesn't apply here as an argument. If there was any relation between the nature and its ways and means, the set theory would be born much sooner than it was. The reason it arrived so late was that no one needed it to climb from the well of the dark ages.

So if you have a finite set of apples in the basket, and you set up logical system that identifies the finite set incomplete, then the set is simply incomplete. The set theory doesn't run on common sense, which is dictated by the real world whose laws we must obey to go by; the set theory runs on strict logic. Any number system is born out of an infinite loop that houses an algorithm. A number system is considered an axiom. So in the traditional way, proving axiom is considered a redundant endeavor. And that what you are trying to do. Just switch to some non-traditional view, and if it is accepted, you are free to prove what you want to prove -- if you know how.
 
doronshadmi said:
Code: 
1 1 1 1 1 1 1 1 1 ... ↔ {1,2,3,4,5,6,7,8,9,...}
↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕  
0 1 0 1 0 1 0 1 0 ... ↔ {2,4,6,8,...}

As can clearly be seen, there is no 1-to-1 correspondence between the natural numbers and the even numbers.
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:) That's what I call icing on the cake . . .

At least there is a partial "1-to-1" correspondence that saves the set theory from a complete and humiliating collapse.
 
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jsfisher said:
No it doesn't, and no it isn't. You would have to be self-delusional to believe that.
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http://www.internationalskeptics.com/forums/showpost.php?p=6808813&postcount=14086 it is a self evident truth without any need of extra words.

You have to be blind in order miss it.

EDIT:

Here is some correction of http://www.internationalskeptics.com/forums/showpost.php?p=6808813&postcount=14086 :

{
00000000000... ↔ { },
11000000000... ↔ {1,2},
10000000000... ↔ {1},
10101010100... ↔ odd numbers {1,3,5,...},
10100000000... ↔ {1,3},
01010101010... ↔ even numbers {2,4,6,...},
01000000000... ↔ {2},
01100000000... ↔ {2,3},
00100000000... ↔ {3},
11111111111... ↔ N numbers {1,2,3,...},
...
}

( 11111111110... ↔ N numbers {1,2,3,...}, was corrected to 11111111111... ↔ N numbers {1,2,3,...}, )
 
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doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=6808813&postcount=14086 it is a self evident truth without any need of extra words.
Click to expand...

Prove it, then. Should be easy if everything is so self-evident to you.

By the way, are there more, less, or the same number (I use that term loosely) of elements in your list as there are 0's and 1's in each list item?

(The correct answer, under your latest set of assumptions, is more. And just like the case with 3 bits of 8 list items, the inverse of the diagonal does in fact exist in the list...just not in the first three. Not everything that's self-evident is the truth.)
 
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