Definition of Surjective Function

What is a Surjective Function?

A surjective function, also known as an onto function, is a type of mathematical function that has a special property. It means that for every element in the target set, there is at least one element in the domain set that maps to it. In simpler terms, it covers the entire range.

Origin of Surjective Functions

The concept of surjective functions has been studied and developed in mathematics over many years. It is a fundamental concept in the branch of mathematics called set theory and is widely used in various areas of mathematics.

Where can you find Surjective Functions in Everyday Life?

Surjective functions can be found in many everyday situations. For example, imagine you have a box of different colored crayons, and you want to give each crayon a label. You decide that each color will have a name, and you assign a name to each crayon based on its color. In this scenario, the function that maps each color to its name is a surjective function, as every color has a name.

Synonyms and Comparison

Synonyms for surjective functions include onto functions and exhaustive functions. Surjective functions are closely related to injective functions (one-to-one functions), which have the property that each element in the target set corresponds to at most one element in the domain set.


In conclusion, a surjective function is a type of mathematical function that covers the entire range. It is widely used in various fields of mathematics and can also be observed in everyday life. Understanding surjective functions helps us describe relationships and mappings between sets.