Posted by T.Gracken on September 11, 2002 at 11:53:52:
In Reply to: Terminology question - for the professors posted by Joel on September 11, 2002 at 10:32:04:
The definition I use (most often) is:
a function is a set of ordered pairs in which no two distinct pair have the same first element.
A more formal definition from most algebra texts is (similar to):
a function is a rule of correspondence between two sets, A and B, such that each element of set A is mapped to exactly one element of set B.
...then a bunch of terminology about domain, range, image, abscissa, ordinate, etc.
In either case, the definition really defines a function as a pairing.
so for the relation you stated, the pairing (a natural number, n, with the sum of natural numbers from 1 to n) is a function.