Concept
What is a bijective function?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"A bijective function is simply one that is both injective and surjective. With an injective function, every y is mapped to by at most one x; with a surjective function, every y is mapped to by at least one x; so with a bijective function, every y is mapped to by exactly one x. Needless to say, the domain and the codomain must have the same cardinality for this to be possible. The function employeeNumber—with employees as the domain and employee numbers as the codomain—is a bijective function. Every employee has an employee number, and every employee number goes with exactly one employee. As a corollary of this, there are the same number of employees as employee numbers. A bijective function is also called a bijection."
Related Ideas
- How can we make a mapping bijective?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What is an injective function?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How can a function be made surjective?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What is a function?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Can the function be injective?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Why is faveSport not injective?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do functions provide a well-defined answer?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What are a function’s meaning, definition, and range?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1