What is Complementary Logic

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In summary: Complimentary logic is not one of those fields. In summary, this conversation does not provide a detailed or precise explanation of how complimentary logic works, or what its potential applications might be.
  • #211
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!
 
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  • #212
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:
Code:
              b   b
             {a , a}    
              .   .  
              |   | 
              |___|_
              |    
                
           
             {a , b}    
              .   .  
              |   | 
              |___|
              |

I opened a new thead for this at:

https://www.physicsforums.com/showthread.php?s=&threadid=14416
 
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<h2>1. What is complementary logic?</h2><p>Complementary logic, also known as dual logic, is a type of logic that involves the use of two opposite or complementary values, typically represented as 0 and 1. It is used in digital systems and circuits to represent and manipulate Boolean values.</p><h2>2. How is complementary logic different from traditional logic?</h2><p>Traditional logic, also known as classical logic, uses a single value to represent true or false statements. Complementary logic, on the other hand, uses two complementary values to represent truth and falsehood. This allows for more complex and versatile operations in digital systems.</p><h2>3. What are some examples of complementary logic?</h2><p>Some common examples of complementary logic include AND, OR, and NOT gates, which are used in digital circuits to perform logical operations on binary inputs. Other examples include XOR, NAND, and NOR gates, which are derived from combinations of the basic gates.</p><h2>4. How is complementary logic used in everyday technology?</h2><p>Complementary logic is used in a wide range of everyday technologies, including computers, smartphones, and other digital devices. It is also used in various electronic systems, such as alarm systems, traffic lights, and industrial control systems.</p><h2>5. What are the advantages of using complementary logic?</h2><p>One of the main advantages of complementary logic is its ability to perform complex logical operations using a small number of basic gates. This makes it a cost-effective solution for digital systems. Additionally, complementary logic is less prone to noise and signal interference compared to traditional logic, making it more reliable in digital systems.</p>

1. What is complementary logic?

Complementary logic, also known as dual logic, is a type of logic that involves the use of two opposite or complementary values, typically represented as 0 and 1. It is used in digital systems and circuits to represent and manipulate Boolean values.

2. How is complementary logic different from traditional logic?

Traditional logic, also known as classical logic, uses a single value to represent true or false statements. Complementary logic, on the other hand, uses two complementary values to represent truth and falsehood. This allows for more complex and versatile operations in digital systems.

3. What are some examples of complementary logic?

Some common examples of complementary logic include AND, OR, and NOT gates, which are used in digital circuits to perform logical operations on binary inputs. Other examples include XOR, NAND, and NOR gates, which are derived from combinations of the basic gates.

4. How is complementary logic used in everyday technology?

Complementary logic is used in a wide range of everyday technologies, including computers, smartphones, and other digital devices. It is also used in various electronic systems, such as alarm systems, traffic lights, and industrial control systems.

5. What are the advantages of using complementary logic?

One of the main advantages of complementary logic is its ability to perform complex logical operations using a small number of basic gates. This makes it a cost-effective solution for digital systems. Additionally, complementary logic is less prone to noise and signal interference compared to traditional logic, making it more reliable in digital systems.

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