Lecture 10: 4/30/2009
Announcements: Ps5 out: Review Problems, not to be turned in
Ps4 solutions out; Ps5 Solutions out later today and Sample midterm solutions
Midterm Tues, May 5; Open Book and Notes; Coverage through relations (today)
Discussion this Friday: Review session (run by me). Bring questions
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Functions (Chapter 3)
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Definition: A function f is a relation on A x B such that
there is one and only one pair a R b for every a ∈A.
We write b=f(a) to mean that (a,b) ∈f.
(Just one way to do it: we could have defined functions as the primitive
and used the function to define the relation, putting in a pair
(a,f(a)) for every a ∈A.)
- We call A the domain of f, Dom(f).
- We call B the *codomain* (or *target*) of f.
Note that this does not mean the set {b: f(a)=b for some a in A}!
That is a different (and important) st called the *Range* (or *image*)
of f. Denote it f(A).
Example 1:
Domain={1,2,3}
f(a) = a^2.
Dom(f) = {1,2,3}
f(A) = {1,4,9}
co-domain: unclear, might be \N, might be \R, ....
Example 2:
Domain = students in this class
b(x) = birthdays, encoded as {1,..,12} x {1..31}.
b(phil) = (7,31)
b(ellen) = (4,1)
