Discrete Math › Section F · Discrete structures revisited › Topic F.2
Functions: injections, surjections, bijections
A function sends every input to exactly one output. Asking whether different inputs can share an output, and whether every possible output is reached, sorts functions into injections, surjections and bijections, and those ideas underlie counting, inverses and even the comparison of infinite sets.
In this topic
- What a function is
- Describing functions
- Image and inverse image
- Injections: no collisions
- Surjections: nothing missed
- Bijections and inverses
- Worked example: classifying functions
- Composition
- Worked example: counting functions
- Floors, ceilings and infinite sets
- Common mistakes to avoid
- Key takeaways
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