One-to-One, Onto and Bijective Functions
For a function $f:A\to B$, $A$ is the domain and $B$ is the codomain. Injectivity distinguishes inputs by their outputs; surjectivity ensures that every declared output is reached.
Summary
For a function , is the domain and is the codomain. Injectivity distinguishes inputs by their outputs; surjectivity ensures that every declared output is reached.
| Property | Requirement | Computing significance |
|---|---|---|
| Injective |
🧠 Key Concepts
- Injective functions
- Surjective functions
- Bijective functions
- Domain and codomain
- Image
- Collisions
- Inverse functions
- Finite cardinality
- Codomain dependence
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One-to-One, Onto and Bijective Functions
📘 Overview Injectivity distinguishes inputs by their outputs, while surjectivity requires every codomain element to be reached. For a function , is the domain and is the codomain; satisfying both properties makes the function bijective.
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