Functions on sets
A function or mapping is a relationship between one set (called
the domain) and another set (called the range). To each element
of the domain is assigned an element of the range. For example:
- The function Score assigns a test scores to each member of the set
Students = {JohnBrown, JaneDoe, JamesChen, ...}.
- The domain of the function Score is Students and the range
is Scores = [0, 100].
We also use the notations:
- Score: Students ® [0,
100]
- Score(JohnBrown) = 90, Score(JaneDoe) = 90.2,
...
In general, a function is a triple
f : X ®
Y,
where X and Y are sets: X is the domain of f,
Y is the range of f, and f is the name of a rule that
assigns the value f(x) in Y to each element x in X.
If x is a variable over X, we also say f is a function
of x. For each element x in the domain, we write f(x)
for the element of the range that is assigned to that value x.
