Please show us how the limit concept is rigorous

[matt grime]

Ah, paradigm shifts, automatic 40 point penalty on the crackpot index. Organic, I have forgotten more about this than you will ever learn, stop patronizing please.

 

[Organic]

automatic 40 point penalty on the crackpot index

1) patronizing? Who gives the points here, me?

2) Please show us a mathematical branch that define organic numbers as I show in my previous post.

3) Once you asked me to explain how N is not a complete collection by show n which is not in N.

My answer is very simple: natural numbers do not exists because of the existence of N, but because of the axioms that define them, N is only the name of the container that its content is infinitely many elements that can never be completed.

 

[matt grime]

How can we demonstrate organic numbers, as you've never defined them?

 

[Organic]

Here they are, in colors, to help you to understand their structures:

Let x be a general notation for a singleton.

When a finite collection of singletons have the same color, we mean that all singletons are identical, or have the maximum symmetry-degree.

When each singleton has its own unique color, we mean that each singleton in the finite collection is unique, or the collection has the minimum symmetry-degree.

Multiplication can be operated only among identical singletons, where addition is operated among unique singletons.

Each natural number is used as some given quantity, where in this given quantity we can order several different sets, that have the same quantity of singletons, but they are different by their symmetrical degrees.

In more formal way, within the same quantity we can define all possible degrees, which existing between a multiset and a "normal" set, where the complete multiset and the complete "normal" set are included too.

If we give an example of transformations between multisetes and "normal" sets, we can see that the internal structure of n+1 > 1 ordered forms, constructed by using all previous n >= 1 forms:

[b]1[/b]
(+1) = [COLOR=Black]{x}[/COLOR]

[COLOR=Blue][b]2[/b][/COLOR]
(1*2)    = [COLOR=Blue]{x,x}[/COLOR]
((+1)+1) = [COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR]

[COLOR=DarkGreen][b]3[/b][/COLOR]
(1*3)        = [COLOR=Darkgreen]{x,x,x}[/COLOR]
((1*2)+1)    = [COLOR=Darkgreen]{[COLOR=Blue]{x,x}[/COLOR],x}[/COLOR]
(((+1)+1)+1) = [COLOR=Darkgreen]{[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR],x}[/COLOR]

[COLOR=Magenta][b]4[/b][/COLOR]
(1*4)               = [COLOR=Magenta]{x,x,x,x}[/COLOR] <------------- Maximum symmetry-degree, 
((1*2)+1*2)         = [COLOR=Magenta]{[COLOR=Blue]{x,x}[/COLOR],x,x}[/COLOR]              Minimum information's 
(((+1)+1)+1*2)      = [COLOR=Magenta]{[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR],x,x}[/COLOR]            clarity-degree
((1*2)+(1*2))       = [COLOR=Magenta]{[COLOR=Blue]{x,x}[/COLOR],[COLOR=Blue]{x,x}[/COLOR]}[/COLOR]            (no uniqueness) 
(((+1)+1)+(1*2))    = [COLOR=Magenta]{[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR],[COLOR=Blue]{x,x}[/COLOR]}[/COLOR]
(((+1)+1)+((+1)+1)) = [COLOR=Magenta]{[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR],[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR]}[/COLOR]
((1*3)+1)           = [COLOR=Magenta]{[COLOR=Darkgreen]{x,x,x}[/COLOR],x}[/COLOR]
(((1*2)+1)+1)       = [COLOR=Magenta]{[COLOR=Darkgreen]{[COLOR=Blue]{x,x}[/COLOR],x}[/COLOR],x}[/COLOR]
((((+1)+1)+1)+1)    = [COLOR=Magenta]{[COLOR=Darkgreen]{[COLOR=Blue]{[COLOR=Black]{x}[/COLOR],x}[/COLOR],x}[/COLOR],x}[/COLOR] <------ Minimum symmetry-degree,
                                              Maximum information's  
                                              clarity-degree                                            
                                              (uniqueness)
[COLOR=Red][b]5[/b][/COLOR]
[COLOR=Red]...[/COLOR]

Can you give me an address of some mathematical brach that researches these kind of relations between multisets and "normal" sets?

Thank you,

Organic

 

[matt grime]

You're just defining certain types of partition functions. Why should we do your research? Do I patronize you? Tell you things you already know? Strange you don't seem to know lots of things. I'm certainly not polite to you, but that's because you don't earn respect from me, not that you'd want to obviously.

 

[Organic]

You're just defining certain types of partition functions

Have you seen before any use of these partition functions as I do?

 

[matt grime]

Yes and no. I have not seen people assign words to things as you do, but then as you never explain what any of those words mean that is highly irrelevant. You don't actually do anything with the things you write down as you admit yourself (and that scores you 50 more points on the crackpot index as well).

 

[Organic]

You don't actually do anything with the things you write down as you admit yourself

Please look here:

http://www.geocities.com/complementarytheory/CATpage.html

and show us an example of how I don't actually do anything with the things I write down.