How Do You Differentiate Between Partial and Total Functions?

[StIgM@]

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

 

[Mark44]

Hello Guys,

I am confused about something.
How do you differentiate the partial and total function?

See Partial 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?

If your CAR set is the set of all Audi automobiles, and PERSON is the set of all people, every car in the CAR set has an owner, but not all owners are people. For example, The Audi Co. owns some of the cars that haven't been shipped to dealers yet. IOW, some of the cars in the CAR set don't map to people in the PERSON set.

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

You can define a set however you want.