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Deeper than primes

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jsfisher said:
Ok, so now it is Cantor's construction method for P(). Fine. Just where do you see that? It is not in the proof anywhere. We all think you are just making stuff up.
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He is mixing between Cantor's theorm about size of set always being smaller than it's power set and Cantor's proof that C>aleph0 using the diagonal approach. Since he does not understand math he thinks these two are the same.
 
doronshadmi said:
Once again you ignore Cantor's construction method of P(S) members, which actually enables to define a 1-to-1 correspondence between S and P(S) members, by using this construction |P(S)| times.

Actually by Cantor's construction method:

S ↔ P(S)
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Your symbolism needs some defining, coz if "↔" is supposed to mean bijection, as you mentioned "1-to-1 correspondence," then S ↔ P(S) is wrong, coz it implies |S| = |P(S)|.

Are you going to help counting? I have this set

S = {1, 2, 3, 4, ...}

and I decided to count all the subsets in P(S) with cardinality equaling 3. But it's a long count . . .

{1 2 3}, {1 2 4}, {1 2 5}, {1 2 6}, . . .
{1 3 4}, {1 3 5}, {1 3 6}, {1 3 7}, . . .
{1 4 5}, {1 4 6}, {1 4 7}, {1 4 8}, . . .
{1 5 6}, {1 5 7}, {1 5 8}, {1 5 9}, . . .
.
.
.

I interlaced the sets the way Cantor did it with rational numbers, but never got to {2 x y}. Do you know how to biject subsets of S where the cardinality of such subsets is C = 3? The only way possible is to organize the above sets in a 3-dim space. It means that in order to arrive at |N| = |P(N)|, you need to organize the power set in (aleph0)!-dim space, where "!" is the factorial. The only person in the universe who could do that is of course you. Take your time . . .
 
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doronshadmi said:
As your guest I am saying to you that the set of natural number is ever increasing (the term "all" is not satisfied) exactly as the set of powersets is ever increasing (the term "all" is not satisfied).
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Again please show what natural number is not a member of the set of all natural numbers. Again you've got nothing to increase in the set of all natural numbers and it is simply you that is "not satisfied" by the term "all" in reference to the natural numbers. The difference between the set of all natural numbers and the set of all power sets is that one is self referential, to some degree (the set of all powersets must include its own power set and the power set of its power set and the power set of that power set and....), while the other is not (no natural number is the set of all natural numbers or the power set of the set of all natural numbers), but I think we have been over that before. So by trying to equate those two sets in your assertion you have simply demonstrated that you don't understand the fundamental differences between the class of all natural numbers and the class of all power sets. The class of all power sets is a proper class (it is not a set) while the class of all natural numbers is a small class (it is a set). It is that specific difference that your are either unaware of or simply ignoring.

doronshadmi said:
Furthermore, Russell's paradox is also an example of the logical inability to determine the exact size of a given infinite set (it is always less or more than any attempt to define its exact size).
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http://en.wikipedia.org/wiki/Proper_class
Paradoxes
The paradoxes of naive set theory can be explained in terms of the inconsistent assumption that "all classes are sets". With a rigorous foundation, these paradoxes instead suggest proofs that certain classes are proper. For example, Russell's paradox suggests a proof that the class of all sets which do not contain themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper.
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Again try learning some set theory instead of just making up your own naive set theory nonsense.
 
doronshadmi said:
Furthermore, Russell's paradox is also an example of the logical inability to determine the exact size of a given infinite set (it is always less or more than any attempt to define its exact size).
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You are completely free to reject some definitions. (Definitions cannot be proven, as you surely know.) And so what is true in A may not be true in B. Some proofs based on a contradiction are crafted the way that the mechanics of the proof is known and the definitions are constructed in favor of the conclusion. Did anyone rain superlatives on Cantor's proof of his theorem, as opposed to his celebrated "diagonal proof?" No, coz the proof is the read-the-fine-print-sort.

So what's the current issue? What is it that you want to say this time?
 
The Man said:
Again please show what natural number is not a member of the set of all natural numbers.
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Any given natural number is a member of the set of natural numbers, where such a set is ever increasing (there is no before being a member or after being a member, but simply a present continuous state).

Since the current mathematical reasoning is essentially based on step-by-step approach, it can't understand the present continuous state, and as a result it naively invents the garbage can of proper classes.

But this naive approach also does not work because the class of all proper classes is unsatisfied, etc. ... ad infinitum.
 
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jsfisher said:
It is not a matter of comprehending your tangle of gibberish you refer to as a post, it is you supporting your claim:

Where is this construction method you claim is in Cantor's proof?​

Either back up this claim or admit you have once again lied.
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jshifher it is right at http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 in front of your single X^2 matrix reasoning.

You simply have to look beyond the matrix in order to get Cantor's construction method, as explicitly shown at http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 .

As long as you can't do it, you are lieing to youself.
 
epix said:
Your symbolism needs some defining, coz if "↔" is supposed to mean bijection, as you mentioned "1-to-1 correspondence," then S ↔ P(S) is wrong, coz it implies |S| = |P(S)|.
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|S| = |P(S)| is right, where both |S| and |P(S)| are equally ever increasing (which is present continuous).
 
epix said:
Are you going to help counting? I have this set

S = {1, 2, 3, 4, ...}

and I decided to count all the subsets in P(S) with cardinality equaling 3. But it's a long count . . .

{1 2 3}, {1 2 4}, {1 2 5}, {1 2 6}, . . .
{1 3 4}, {1 3 5}, {1 3 6}, {1 3 7}, . . .
{1 4 5}, {1 4 6}, {1 4 7}, {1 4 8}, . . .
{1 5 6}, {1 5 7}, {1 5 8}, {1 5 9}, . . .
.
.
.
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As for this part of your post, first try to get this part
doronshadmi said:
The same 1-to-1 correspondence construction method works also in the case of infinitely many objects, where in this case P({}, ... , {1,2,3,...}) is the power set of {1,2,3,...}, and also in this case we are able to define a 1-to-1 correspondence between 1 to {}, 2 to {1,2,3,...}, and any natural number > 2 with any P({}, ... , {1,2,3,...}) member between {} and {1,2,3,...}.
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of http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 .
 
doronshadmi said:
jshifher it is right at http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 in front of your single X^2 matrix reasoning.
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Once again, Doron mistakes his own gibberish and faulty reasoning for substance. He refuses to support his claim, and it was obvious his claim was bogus to begin with. We all are left wondering* why he is so invested in lying.

The proof for Cantor's Theorem contains neither a construction method for the power set of any set, nor one for a bijective mapping between the natural numbers and any power set.

Doron was willfully lying when he claimed otherwise.




*Note the use of present progressive tense denoting an action that is going on now, continuing from the past and progressing into the future.
 
jsfisher said:
Once again, Doron mistakes his own gibberish and faulty reasoning for substance. He refuses to support his claim, and it was obvious his claim was bogus to begin with. We all are left wondering* why he is so invested in lying.

The proof for Cantor's Theorem contains neither a construction method for the power set of any set, nor one for a bijective mapping between the natural numbers and any power set.

Doron was willfully lying when he claimed otherwise.




*Note the use of present progressive tense denoting an action that is going on now, continuing from the past and progressing into the future.
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Another failure of jsfisher's step-by-step reasoning, which is closed under a single X^2 matrix, and can't get anything beyond it in terms of ever increasing present continuous.

As a result he can't get http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 .

As long as you can't do it, you are lieing to yourself, jsfisher.

EDIT:

jsfisher said:
*Note the use of present progressive tense denoting an action that is going on now, continuing from the past and progressing into the future.
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Note the fact that jsfisher's step-by-step reasoning forces past and future on present continuous.

He simply can't comprehend the simultaneity of "continuing from the past" AND "progressing into the future" , exactly because he uses only a step-by-step reasoning.
 
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doronshadmi said:
He simply can't comprehend the simultaneity of "continuing from the past" AND "progressing into the future" , exactly because he uses only a step-by-step reasoning.
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It only takes one step to define, for example, the set of all positive integers. You're the who makes a meal of it by viewing it as some sort of continuous process of many steps.
 
doronshadmi said:
Any given natural number is a member of the set of natural numbers, where such a set is ever increasing (there is no before being a member or after being a member, but simply a present continuous state).
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So again there is noting to increase in your "ever increasing" set. Again that is simply your problem Doron, you want to claim the "set is ever increasing" without anything changing. Again you simply remain the staunchest opponent of just your own notions.


doronshadmi said:
Since the current mathematical reasoning is essentially based on step-by-step approach, it can't understand the present continuous state, and as a result it naively invents the garbage can of proper classes.
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The assumption that all classes are sets is simply inconsistent. Simply making your notion of a set also inconsistent by claiming it is "ever increasing" without anything changing doesn't make the assumption that all classes are sets any less inconsistent. Not only does it fail to even address the inconsistency of the assumption that all classes are sets it isn't even self consistent as a set that doesn't change doesn't increase (or even decrease) in any way.

Again


The Man said:
By all means please explain to us the difference between increasing and decreasing with “no past (before) and no future (after)”?
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doronshadmi said:
But this naive approach also does not work because the class of all proper classes is unsatisfied, etc. ... ad infinitum.
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Once again it is simply you that remains " unsatisfied, etc. ... ad infinitum".
 
doronshadmi said:
Let me help you sympathic.

You simply do not get http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419.

Furthermore, Cantor's diagonal method is equivalent to http://www.internationalskeptics.com/forums/showpost.php?p=6925404&postcount=14419 , but since you do not understand Math you are unable to comprehend this equivalency.
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Anything is possible in a dream and even gibberish makes sense. Wake up to to reality or keep on dreaming. Your choice.
 
doronshadmi said:
Another failure of jsfisher's step-by-step reasoning
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You make many, many bogus claims. You can support none of them. This is just another in a long series.

Now, about that construction method that does actually exist. In what step of the proof do you claim it is? Can we at least narrow your fantasy to one or two steps?
 
The Man said:
you want to claim the "set is ever increasing" without anything changing.
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The Man, your inability to get the simultaneity of the invariance of pi AND the variance of curvature among a collection of infinitely many circles, is equivalent to your inability to get the ever increasing collection of natural numbers as a present continuous state.
 
zooterkin said:
It only takes one step to define, for example, the set of all positive integers. You're the who makes a meal of it by viewing it as some sort of continuous process of many steps.
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There are no steps and no process at present continuous state as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6941558&postcount=14458 .

Like jsfisher, The Man, epix and sympathic, you don't comprehend the simultaneity of "continuing from the past" AND "progressing into the future"
 
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sympathic said:
Anything is possible in a dream and even gibberish makes sense. Wake up to to reality or keep on dreaming. Your choice.
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This is the best advice that you can give to yourself, it is about time to wake up from Cantor's "paradise" dream.
 
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