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How are functions written as ordered triples?

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In a function, I know that domain $A$ and codomain $B$ are not restricted to sets. They can be proper classes. In that case, how can we write functions as ordered triple? I used to think that in order to write $<f,A,B>$, each of them ($f$, $A$, and $B$) must be elements. In Pinter’s “Set Theory”, a function is defined as ordered triple, but he also says that $A$ and $B$ can be proper classes. So I have a confusion regarding this. Then, what is wrong with my opinion?


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