- #141
matt grime
Science Advisor
Homework Helper
- 9,426
- 6
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.
1) patronizing? Who gives the points here, me?automatic 40 point penalty on the crackpot index
[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]
Have you seen before any use of these partition functions as I do?You're just defining certain types of partition functions
Please look here:You don't actually do anything with the things you write down as you admit yourself
The limit concept is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It is used to determine the value that a function approaches as the input gets closer and closer to a specific value.
The limit concept is used to define important concepts in calculus, such as continuity, derivatives, and integrals. It allows us to analyze the behavior of functions and make predictions about their values at specific points.
A rigorous limit is one that is well-defined and can be proven to exist using mathematical principles. This means that the limit is not simply an approximation, but rather a precise value that can be calculated and proven to be correct.
The limit concept is proven to be rigorous through the use of mathematical definitions and theorems. These definitions and theorems provide a framework for understanding the concept and proving its validity.
One example of a rigorous limit is the limit of the function f(x) = x^2 as x approaches 2. This limit can be proven to exist and have the value of 4 using the formal definition of a limit and the properties of limits.