surjection

9.9

A function where every element of the output set has some input that maps to it

noun
/sɜrˈdʒɛkʃən/

Specialized

: sobreyectiva

A common example of a surjection is the function that assigns each student to at least one course they are enrolled in.

Examples

To prove the function is a surjection, we must show that for every output value, there is a corresponding input value that maps to it.
for the number of surjections and for each possible R.
In mathematics, a surjection ensures that every element in the target set is paired with at least one element from the starting set.

Synonyms

onto function

vssurjection

Specialized

9.6

A rule that gives every possible output from some input

is the standard definition phrased with codomain terminology

surjective function

vssurjection

Specialized

9.9

A rule that gives every output value at least one input value

is the same but prefers codomain wording instead

Surface Forms

surjection singular

surjections plural

Morphology

surjection = surject (opaque) = sur + ject + ion

The noun is formed by the regular suffixation of '-ion' to the verb 'surject', creating the expected noun meaning.

Etymology

Surjection comes from the parts sur- meaning 'over' and -ject meaning 'to throw', the same root you see in inject and project. So think of 'throwing over' every target: a surjection is a function that 'hits' every element in the target set.