Circular definition of functions as ordered triples?

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poochie_d
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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.
 

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poochie_d said:
But ordered tuples are really functions from [itex]\{1, ..., n\}[/itex] to (whatever set under consideration), right?

No, this is not true. The ordered tuple (a,b) is defined as {{a},{a,b}}. It's not defined as a function.
 
But aren't tuples other than the ordered pair defined as functions, so that the definition of functions as triples would still be circular?
 
poochie_d said:
But aren't tuples other than the ordered pair defined as functions, so that the definition of functions as triples would still be circular?

No, triples can be defined as

[tex](a,b,c)=((a,b),c)[/tex]

And the definition of a function only uses ordered pairs and triples. So there is nothing circular.
 
Oh I think I get it now. Thanks micromass!