Understanding Partial and Total Functions in Set Theory

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SUMMARY

This discussion clarifies the distinction between partial and total functions in set theory, specifically in the context of defining a function from a set of cars (CAR) to a set of persons (PERSON). A total function requires that every element in the domain (CAR) has a corresponding element in the codomain (PERSON), while a partial function does not. In the example provided, the function CAR → PERSON is considered partial if not every car has an owner, thus not utilizing the entire domain.

PREREQUISITES
  • Understanding of set theory concepts, including sets and functions.
  • Familiarity with the definitions of partial and total functions.
  • Basic knowledge of mathematical notation and terminology.
  • Concept of domain and codomain in functions.
NEXT STEPS
  • Study the definitions and examples of partial and total functions in set theory.
  • Explore the implications of domain and codomain in mathematical functions.
  • Learn about function mappings and their applications in real-world scenarios.
  • Investigate the role of functions in programming, particularly in functional programming languages.
USEFUL FOR

Mathematicians, computer scientists, and students studying set theory or functional programming who seek to understand the application of partial and total functions in various contexts.

StIgM@
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Hello Guys,

I am confused about something.
How do you differentiate the partial and total function?
I know that partial functions do not use the whole domain, but how do you know if the whole domain will be used?

For example, I want to define an operation for the AUDI car company and I want to define the function between audi car and owner. So I declare a set CAR and a set PERSON.
The function CAR ---> PERSON is partial or total and why?


Also, when I declare a set do I mean that the set can contain all the items that might exist in the world?

Thanks
 
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I have no idea what your function is supposed to do. It takes some kind of car, and assigns to it a person that owns that particular car?
 

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