How Does Complementary Logic Redefine Mathematical Infinity?

[Hurkyl]

Paradigms don't change, they shift. When someone comes up with a revolutionary new way to do things or to think about things, it's just that... a NEW way to do things or to think about things.

If, indeed, you are bringing about a paradigm shift in mathematics, you do not alter any old mathematics!

 

[Organic]

No theoretical system can survive without being aware to its limitations.

It means that any x output can be only a model(X) input.

Shortly speaking, x=model(X).

Math is first of all a form of theory, therefore any concept that can be used by it is only a model(CONCEPT).

For example, let us take infinity concept.

If INF is infinity itself (= actual infinity) , then inf=model(INF)=potential infinity.

Please look at this model for better understanding:
http://www.geocities.com/complementarytheory/RiemannsLimits.pdf

In this way we first of all aware to our input limitations, which are:

No input = model(EMPTINESS) = lowest limit.

No input = model(FULLNESS) = highest limit.

If we translate this to set's representation then:

{} content = model(EMPTINESS) = lowest limit.

{__} content = model(FULLNESS) = highest limit.

Between these limits ({},{__}) we can find inf=model(INF)=potential infinity, where inf has two input forms:

{.} = singleton, which is a localized element.

{.__.} = non-singleton, which is a non-localized element (connect at least two different singletons).

{.} and {._.} can appear in two basic collections:

Collection {a, b, c} is finitely many elements.

Collection {a, b, c, ...} is infinitely many elements (=inf) .

Any non-empty collection which is not a singleton, is an association between {.} and {._.}, for example:

              b   b
             {a , a}    
              .   .  
              |   | 
              |___|_
              |    
                
           
             {a , b}    
              .   .  
              |   | 
              |___|
              |

I opened a new thead for this at:

https://www.physicsforums.com/showthread.php?s=&threadid=14416