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On limits

could you do everyone a favour? when you're about to switch and start talking about mathematics as only you consider it and not as the rest of the world understands it could you give us a signal? we prove things in context. if you're just going to artificially change the context and the rules at least have the decency to let us know so we can just file it under 'organic goes off on one again' for instance we state d is fixed (it is |a-b| and they are fixed), so if you're going to use another incompatible definition of it give us a heads up.

 'organic goes off on one again'
I think that the one who goes on an off is you Matt, for example:

By your method, infinitely many elements have the same property like finitely many elements, and this is the reason that you have no problem to use words like 'all' and 'complete' together with infinitely many elements.

But sometimes you use the open interval Idea, and then no infinitely many elements can reach the limit.

Trough my point of view, a collection of infinitely many elements cannot be completed by definition, therefore I call it an open collection.
 Recognitions: Homework Help Science Advisor Then you aren't using any of those words with the definition attached to them that other people give them. Therefore it is no wonder you are constantly saying things that are wrong on appearance, as everyone keeps telling you, you are using words with a different meaning from everyone else, and hte fact that what they say is 'wrong' if given your meaning to the words is not a particularly relevant issue because of your misuse of the terms.
 Have you heard about the words "Paradigm Shift"? Paradigm shift is like a mutation where mutation changes the system from within and not just adding another pretty thing to the existing system without changing any fundamental concept of it. For example my organic numbers: 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: Code: 1 (+1) = {x} 2 (1*2) = {x,x} ((+1)+1) = {{x},x} 3 (1*3) = {x,x,x} ((1*2)+1) = {{x,x},x} (((+1)+1)+1) = {{{x},x},x} 4 (1*4) = {x,x,x,x} <------------- Maximum symmetry-degree, ((1*2)+1*2) = {{x,x},x,x} Minimum information's (((+1)+1)+1*2) = {{{x},x},x,x} clarity-degree ((1*2)+(1*2)) = {{x,x},{x,x}} (no uniqueness) (((+1)+1)+(1*2)) = {{{x},x},{x,x}} (((+1)+1)+((+1)+1)) = {{{x},x},{{x},x}} ((1*3)+1) = {{x,x,x},x} (((1*2)+1)+1) = {{{x,x},x},x} ((((+1)+1)+1)+1) = {{{{x},x},x},x} <------ Minimum symmetry-degree, Maximum information's clarity-degree (uniqueness) 5 ... Can someone give me an address of some mathematical brach that researches these kind of relations between multisets and "normal" sets? Thank you, 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.
 Recognitions: Homework Help Science Advisor How can we demonstrate organic numbers, as you've never defined them?
 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: Code: 1 (+1) = {x} 2 (1*2) = {x,x} ((+1)+1) = {{x},x} 3 (1*3) = {x,x,x} ((1*2)+1) = {{x,x},x} (((+1)+1)+1) = {{{x},x},x} 4 (1*4) = {x,x,x,x} <------------- Maximum symmetry-degree, ((1*2)+1*2) = {{x,x},x,x} Minimum information's (((+1)+1)+1*2) = {{{x},x},x,x} clarity-degree ((1*2)+(1*2)) = {{x,x},{x,x}} (no uniqueness) (((+1)+1)+(1*2)) = {{{x},x},{x,x}} (((+1)+1)+((+1)+1)) = {{{x},x},{{x},x}} ((1*3)+1) = {{x,x,x},x} (((1*2)+1)+1) = {{{x,x},x},x} ((((+1)+1)+1)+1) = {{{{x},x},x},x} <------ Minimum symmetry-degree, Maximum information's clarity-degree (uniqueness) 5 ... Can you give me an address of some mathematical brach that researches these kind of relations between multisets and "normal" sets? Thank you, Organic
 Recognitions: Homework Help Science Advisor 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.

 You're just defining certain types of partition functions
Have you seen before any use of these partition functions as I do?
 Recognitions: Homework Help Science Advisor 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).

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