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({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused about set-theoretic definition of a function

**Physics Forums | Science Articles, Homework Help, Discussion**