4.3 Properties of Functions
- A function f: X → Y is one-to-one or injective if f maps different elements in X to different
elements in Y
- Ex. function maps employees to offices
- If a function is one-to-one, no one has to share an office
- If a function is onto, then there are no empty offices and the company’s space is well
utilized
- A function f: X → Y is onto or surjective if the range of f is equal to the target Y
- A function is bijective if it is both one-to-one and onto → bijection
- Aka. one-to-one correspondence
- A function f: X → Y is one-to-one or injective if f maps different elements in X to different
elements in Y
- Ex. function maps employees to offices
- If a function is one-to-one, no one has to share an office
- If a function is onto, then there are no empty offices and the company’s space is well
utilized
- A function f: X → Y is onto or surjective if the range of f is equal to the target Y
- A function is bijective if it is both one-to-one and onto → bijection
- Aka. one-to-one correspondence
