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Deeper than primes

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doronshadmi said:
jsfisher said:
That would be the post where you provided two separate mappings from S to P(S). The first was A->{A}; the second was A->{}. Neither mapping is a bijection between the members of {A} and P({A}).
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That is again your reasoning, which simply can't get the simple fact that natural numbers are not limited to any particular collection and therefore, there is a 1-to-1 correspondence between the natural numbers and any given collection of different objects, whether the given collection has finite or infinite amount of objects.
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You have reading comprehension issues again, Doron. Bijective, not injective (one-to-one), and between the members of {A} and P({A}), not the natural numbers.

Be that as it may, there is not injective mapping from the natural numbers to P({A}), either, so even accepting your non-sequitur response, you are still wrong.

In other words, by using Cantor's construction method...
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That being the construction method that exists nowhere in reality
...on {{},{A}} case, there is a bijedction between the natural numbers and {{},{A}} as follows:

Case 1:
-----------------------
A ↔ {A} | Provides 1 ↔ {}
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Not a bijection.

Case 2:
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A ↔ { } | Provides 2 ↔ {A}
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Also, not a bijection.

...and this is one and only one mapping.
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And 1 ↔ {} / 2 ↔ {A} is not a bijection. Not an injection, either.

Doron, you have failed yet again and in multiple ways.
 
jsfisher said:
Doron, you have failed yet again and in multiple ways.
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jsfisher, since your reasoning prevents from you to get Cantor's construction method you are failing to get

A ↔ {A} | Provides 1 ↔ {}

A ↔ { } | Provides 2 ↔ {A}

as a one mapping.
 
jsfisher said:
The comprehension failure is yours and yours alone. Nowhere in that post to you point out there this so-called construction method occurs in the proof to Cantor's Theorem.
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That is only the result of your imaginary reasoning on your mind.

You simply can't get out of it, and therefore do not understand any possible reasoning beyond it.
 
doronshadmi said:
jsfisher, since your reasoning prevents from you to get Cantor's construction method you are failing to get

A ↔ {A} | Provides 1 ↔ {}

A ↔ { } | Provides 2 ↔ {A}

as a one mapping.
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"One mapping"? Inventing yet more terms, I see. That sort of fits with the construction method you simply invented. There is no such construction method provided by Cantor.

Be that as it may, neither of the mappings you present are injective nor bijective.
 
Jsfisher, along this thread you are missing a very simple fact, which is:

Any given set it is first of all a collection of different objects.

In other words, a set has more than one object only if it is a simultaneous result of connectivity AND isolation.

Imbalance between connectivity AND isolation is resulted by sets with different amount of objects w.r.t each other, but by using balanced methods, it is possible to show a bijection between any two sets.

Cantor's construction method is a straightforward technique, which demonstrates the balance between any two sets, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6951142&postcount=14492, and this balance can't be understood if the used reasoning gets it as isolated cases ( exactly as jsfisher does by isolate the mappings, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=6951775&postcount=14502 ).
 
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doronshadmi said:
Jsfisher, along this thread you are missing a very simple fact, which is:

Any given set it is first of all a collection of different objects.
Click to expand...

Why do you belabor this trivial thing? Has anyone said otherwise?

In other words, a set has more than one object only if it is a simultaneous result of connectivity AND isolation.
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This statement, on the other hand, is meaningless doronetics.

Imbalance between connectivity AND isolation is resulted by sets with different amount of objects w.r.t each other, but by using balanced methods, it is possible to show a bijection between any two sets.
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And yet you have repeated failed in all attempts to present a bijection.

Cantor's construction method...
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...which exists only in the imagination of Doron and not in anything Cantor presented...
...is a straightforward technique, which demonstrates the balance between any two sets, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6951142&postcount=14492, and this balance can't be understood if the used reasoning gets it as isolated cases ( exactly as jsfisher does by isolate the mappings, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=6951775&postcount=14502 ).
Click to expand...

We understand it just fine. It is awash with the typical gibberish, contradiction, and nonsense that is your trademark, Doron. That's very clear.
 
jsfisher said:
This statement, on the other hand, is meaningless doronetics.
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This statement, on the other hand, cannot be comprehended by your rigid isolating reasoning.


jsfisher said:
And yet you have repeated failed in all attempts to present a bijection.
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And yet you have repeated failed in all attempts to get the bijection by using
your rigid isolating reasoning.

jsfisher said:
...which exists only in the imagination of Doron and not in anything Cantor presented...
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...which you share with many other rigid minds like you that have no ability to comprehend Cantor's construction method.



jsfisher said:
We understand it just fine.
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No, you don't. You get only the isolated aspect of Cantor's construction method.
 
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doronshadmi said:
...which you share with many other rigid minds like you that have no ability to comprehend Cantor's construction method.
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So, why are you unable to show us where Cantor presented his construction method? Surely it's there somewhere. Just point to the place in the proof where it occurs.
 
doronshadmi said:
Yes jsfisher, it is one bijective mapping, and your isolated reasoning can't comprehend it.
Click to expand...


Let's review. Doron presented us with two mappings:

A ↔ {A} | Provides 1 ↔ {}
A ↔ { } | Provides 2 ↔ {A}​

We have first A ↔ {A} and A ↔ { }. That's not bijective. Heck, that's not even functional since A has two possible mappings. No bijection here.

Then we have 1 ↔ {} and 2 ↔ {A}. Also not bijective, at least not between the natural numbers and the members of P({A}). There'd need to be a mapping for all of the natural numbers, not just two of them. No bijection here, either.

Another Doron masterpiece of failure.
 
doronshadmi said:
By using a cross-contexts reasoning, let us use Cantor's construction method...
Click to expand...
treeax.png

...By using Cantor's construction method with the members of {1,2,3} and the same amount of members taken from P({1,2,3}), one enables to explicitly define each P({1,2,3}) member...
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tercka.png

1 <----> thiefL
2 <----> "i'll be back"
3 <----> thiefR


Note: Doron, this is an atheist board so I would recommend using that cross-context reasoning sparingly.
 
jsfisher said:
Let's review. Doron presented us with two mappings:

A ↔ {A} | Provides 1 ↔ {}
A ↔ { } | Provides 2 ↔ {A}​

We have first A ↔ {A} and A ↔ { }. That's not bijective. Heck, that's not even functional since A has two possible mappings. No bijection here.

Then we have 1 ↔ {} and 2 ↔ {A}. Also not bijective, at least not between the natural numbers and the members of P({A}). There'd need to be a mapping for all of the natural numbers, not just two of them. No bijection here, either.

Another Doron masterpiece of failure.
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jsfisher you simply repeat on your separation approach of the two mappings (you get only one mapping at a time), so by using this separation method, there is no wonder that you can't define the bijection between 1,2 and {},{A} objects.

Your problem is found right there:
jsfisher said:
doronshadmi said:
Jsfisher, along this thread you are missing a very simple fact, which is:

Any given set it is first of all a collection of different objects.
Click to expand...
Why do you belabor this trivial thing? Has anyone said otherwise?
Click to expand...
jsfisher, it is a trivial thing for you exactly because you are not using your reasoning in order really understand what enables the existence of a collection of different objects.

For you an expression like "connectivity AND isolation" is meaningless exactly because your reasoning is not involved in any further research of the fundamental conditions that enable the existence of sets (you take their existence obviously).

A direct result of this (indeed) trivial approach, prevents from you to understand the non-trivial conditions that enable the existence of sets, in the first place.

In other words, jsfisher, What You See Is What You Get, and in this case you see triviality and therefore there is no wonder that you indeed get triviality.

-------------------------------------

By understanding sets as a result of connectivity AND isolation, one enables to use methods, which are inaccessible to any one that does not research the fundamental conditions that enable the existence of sets.

One of these methods is Cantor's construction method, which is based on the fact that sets are the results of connectivity AND isolation.

For example, finite sets are the result of stronger isolation w.r.t connectivity under connectivity AND isolation comprehensive and one framework.

Being a finite set is being isolated by strict amount of objects, such that there can be differences of these amounts under comparison (where comparison is not possible without the connectivity accept among isolated objects, under connectivity AND isolation comprehensive and one framework).

By using Cantor's construction method as a tool of connectivity AND isolation comprehensive and one framework, one enables to define any wished degree of mapping between any two given sets, where the set of natural numbers is used as a dynamic measurement tool for any mapping degree between two sets with different objects.

This dynamic measurement is useful for both finite or infinite sets, where in the case of finite sets, the aspect of connectivity is expressed as the tendency for balance between the considered sets, where this balance is fully expressed as a bijective mapping.

In the case of finite sets, this mapping has finite amount of results, which exist between non-bijection and bijection.

In the case of infinite sets, this mapping has infinite amount of results, which exist between non-bijection and bijection.

In both cases Cantor's construction method is used as the main tool.

Furthermore, by understanding that connectivity is a building-block of sets exactly as isolation is a building-block of sets under connectivity AND isolation comprehensive and one framework, one enables to understand that both building-blocks must be true (both of them are present) otherwise "connectivity AND isolation" is a false proposition.

By understanding this logical truth, one enables to understand that no amount of isolated objects is connectivity, and as a result given any set, its amount can't be summed into connectivity, such that given any set, it is an ever increasing form of existence (abstract or not).
 
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epix said:
[qimg]http://wwwdelivery.superstock.com/WI/223/1830/PreviewComp/SuperStock_1830-3365.jpg[/qimg]

... in Folsom prison.

[qimg]http://thebsreport.files.wordpress.com/2010/07/escape.jpg[/qimg]
Click to expand...
There is nothing like personal experience, isn't it epix?
 
doronshadmi said:
jsfisher you simply repeat on your separation approach of the two mappings (you get only one mapping at a time), so by using this separation method, there is no wonder that you can't define the bijection between 1,2 and {},{A} objects.
Click to expand...

A bijection between 1, 2 and {}, {A} is trivial. It is also not what you claimed.

You claimed there was a bijection between (1) the set of natural numbers and any power set and (2) any set and its power set. You have failed in every attempt to show either of these things.

...By using Cantor's construction method...
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This is another of your bogus claims. Cantor provided no such method.
 
jsfisher said:
A bijection between 1, 2 and {}, {A} is trivial. It is also not what you claimed.
Click to expand...
Again you demonstrate your trivial reasoning by get this bijection as trivial.

Furthermore, now you change your claim about the non-bijection between 1,2 and {},{A} as you wrote in http://www.internationalskeptics.com/forums/showpost.php?p=6951775&postcount=14502 .

jsfisher, you do not have the slightest idea about what I claim exactly because you do not have the slightest idea of what a set is.

jsfisher said:
You claimed there was a bijection between (1) the set of natural numbers and any power set and (2) any set and its power set. You have failed in every attempt to show either of these things.
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(1) and (2) are shown in http://www.internationalskeptics.com/forums/showpost.php?p=6951142&postcount=14492 .

You also unable to comprehend:

http://www.internationalskeptics.com/forums/showpost.php?p=6928575&postcount=14425

http://www.internationalskeptics.com/forums/showpost.php?p=6916077&postcount=14361

http://www.internationalskeptics.com/forums/showpost.php?p=6918253&postcount=14366


jsfisher said:
This is another of your bogus claims. Cantor provided no such method.
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Yes, he provided such a method, exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6951142&postcount=14492 .

You are unable to get what I say exactly because you do not understand what enable sets, in the first place.
 
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doronshadmi said:
Again you demonstrate your trivial reasoning by get this bijection as trivial.
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You are the only one here who cannot see just how trivial it is.

Furthermore, now you change your claim about the non-bijection between 1,2 and {},{A} as you wrote in http://www.internationalskeptics.com/forums/showpost.php?p=6951775&postcount=14502 .
Click to expand...

Please pay attention. It is not a bijection between the natural numbers and {},{A}. The natural numbers include more than just 1 and 2.

...
Yes, he provided such a method, exactly as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6951142&postcount=14492 .
Click to expand...

Please show us where Cantor provided such a method. Stop showing us your bogus posts; show us Cantor's work.
 
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