Definition: Surjective Function

Definition: A function f: A \rightarrow B is surjective if for every element “b” in B, there is some element “a” in A such that f(a)=b. //

This simply means that our function “hits” every element in the set that it’s mapping to (i.e., its codomain).  In our school dance example, this idea corresponds to the scenario in which every girl has at least one dance partner.  Note the “at least” here, which is included because the definition of surjectivity makes no reference to how many elements in A are sent to “b” in B, but rather that there always is at least one.  Also note that this has to hold for every element in B.

For more on surjectivity, take a look at lesson 7.

Back to Glossary

Back to Lessons

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s