We make the following proposal to the Mathematical community.
Anyone well versed in Logic and Set Theory will be familiar with the concept of cardinality and the nature by which the cardinality of the real numbers R as a whole over the natural numbers N was established.
There is a clear reason why the diagonalisation argument [Diag(N,R)] works in the way of the above establishment.
Being able to pinpoint the reason, will have the effect of being able to prove \kappa{S_1} > \kappa{S_2} for sets S_1 and S_2 having the necessary characteristics, by performing : [Diag(S_1,S_2)].
To aide in clarifying the above, we have attached a diagram.
We will be presenting the above idea in a conference in India.
Dear Rajah Iyer ,
By ( diagonalization argument), did you mean the Cantor's diagonal argument ??
Also, where is the new approach?? Your short statements are not enough to show your idea.
Hope you can show your results later when the conference is done.
Dear Rajah,
sorry, you are a little too late. The diagonal argument (it´s the second!) of Cantor gets disproved.
See: www.mathe-neu.de
(page 2 /click left: Logik des Formalismus; scroll down -> English: 3. Cantor, 4. Proof, 5. Cantor 3)
Nevertheless inside you argumentation are mistakes.
1. You didn’t show any logical development of the relationships.
2. You add sequences of numbers (zeros) to an infinite sequence.
[very shortened: 11… –> 101…]
3. All sequences you list are such of a normal development (reaching all
combinations).
Don’t get the blame. Best wishes, Peter
Dear Peter I do not add 0's to sequences (common mistake) in the flawed interpretation/understanding of what it is that is being described and it is not : "[very shortened: 11… –> 101…] ".
As for your claim regarding Cantor, kindly provide a valid peer reviewed citation.
Dear Issam: Yes I do mean the Diagonal Argument of Cantor and I will gladly elaborate as best as I can after the preparation of the conference paper which I will share with you.
Rajah Iyer
Quote: `As for your claim regarding Cantor, kindly provide a valid peer reviewed citation.´ End quote
Why should I do so? Does research and it´s truth come by peer reviewing?
Why do you make a proposal when not willing to cummunicate about?
Did you understand my papers? Do you know the difference between real and irrational? Which of your sequences is an irrational one?
Where could we find the functions N->R, N->SR and SR->R in your proposal?
What would your approach be for if it is proved that the naturals are able to count the reals (infinite sets couldn’t be categorized in quantity, see Cantor’s first diagonal argument)?
See all naturals including a single zero sequence (10, 20, …) as a subset. The rest could count an infinite set (whole the naturals for example). The first subset also is infinite (for use in counting).
See all naturals including two zeros in sequence (100, 200, …) as the next subset …
If you were able to follow Cantor (slash 2), you would be able to follow my papers.
Why so complicated? Every `inversed´ sequence 110011... —> 001100... shows to split all of them half and half by the function `invers´! What is new at your subsets?
Rajah Iyer
The idea of increasing sequences of equal types (zero´s) for creating excluded subsets is an idea of my papers (Cantor, Proof, Cantor 3).
The copyright started 2010/2013.
My papers represent another conclusion but I will not allow you to present the main idea as your work.
The German versions of my papers were present at RG for the ask for help in translation (Who likes to tanslate the counter-proof of the diagonal slash argument from German to English? / Is contradiction between Cantor slash1 and slash2 already known?).
Please accept my copyright or I have to use all possible tools to hold my rights.
You may ask for an acceptance for quoting my papers.
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