I have read that a function f: A -> B can be defined as an ordered triple of sets (A,B,X), where X is the set of all ordered pairs [itex] X = \{(a,f(a)) \in A \times B\}. [/itex] But ordered tuples are really functions from [itex]\{1, ..., n\}[/itex] to (whatever set under consideration), right? So isn't this a circular definition? Or is there a more basic definition of functions that does not involve tuples? Any help would be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# Confused about set-theoretic definition of a function

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