# Definition: Codomain

Definition: Let f be a function.  The codomain of f is simply the set in which f takes its values.  Namely, if f is a function from A to B, denoted $f:A\rightarrow B$,  then B is the codomain of f.

This definition is super simple.  It is a prime example of when mathematicians just need to come up with a word to describe something that is very common.  The reason we need to come up with somewhat fancy words for extremely common ideas is that the more common an idea is, the more often it is used, and therefore the more likely it isto be confused with other words.  Thus, if we give fancy names to common ideas, it’ll be less likely for our definitions to overlap (after all, there are many more mathematical concepts than there are unique and plausible English words to describe them, so eventually we’ll need to “double up” our definitions and just rely on context to clarify which we’re talking about).

For more on codomains, refer to lesson 6.

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