A dyadic relation which qualifies as a function may then enjoy a number of further distinctions.
For example, the function shown below is neither total nor tubular at its codomain so it can enjoy none of the properties of being surjective, injective, or bijective.
An easy way to extract a surjective function from any function is to reset its codomain to its range. For example, the range of the function above is If we form a new function that looks just like on the domain but is assigned the codomain then is surjective, and is described as a mapping onto
The function is injective.
The function is bijective.
- Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References
- Logic Syllabus • Relational Concepts • Relation Theory • Relative Term