Understanding Partial and Total Functions in Set Theory

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Partial functions are defined only for some elements of the domain, while total functions are defined for every element. In the example of defining a function between the set CAR and the set PERSON, it is a partial function if not every car has an owner assigned. To determine if a function is total, one must assess whether every element in the domain has a corresponding element in the codomain. When declaring a set, it does not imply that it contains all possible items in existence, but rather a specific collection defined by the context. Understanding these distinctions is crucial for accurately modeling relationships in set theory.
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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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