| Math 323 (Laetsch) |
Defining Functions and Codomains |
|
WARNING: Defining functions and
Codomains
Remember that if you are trying to define a function f from a
set S to a set T, you cannot simply write a
formula for f (or give a “rule” for
f ) and then pretend that it is automatically true
that your f is indeed a function from S to
T:
f : S → T.
- First, of course, you have to be sure that the formula you give for
f really defines f(x) for every element
x of S. Often this is so obvious it does not
need special mention, but don't forget at least to think about it.
- Then — the part that is often forgotten — you have to be sure that
T is an appropriate codomain for your f. This
means that every output of f (from inputs in S)
is in the set T. This is often easy to prove (a first year
algebra or trig problem, e.g.), but it cannot be ignored completely.
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Last modified 3/06/08