Function index

This folder contains the local vocabulary for functions: rules, domains, codomains, inverse functions, and special mapping properties. Functions are the central object behind calculus, differential equations, probability models, ML models, and many physics laws.

Local notes

• Function — definition and mapping-property overview.
• Domain — allowed inputs.
• Codomain and range — declared target set versus outputs actually reached.
• Inverse functions — reversing a function when possible.
• Injective function — one-to-one mappings.
• Surjective function — onto mappings.
• Bijective function — both one-to-one and onto.
• Mapping — assignment between sets.
• Relation — the broader set-theoretic idea behind functions.

Nearby foundations

• Set theory index and Set for the underlying language.
• Number sets and Interval for common domains.
• Euler’s number, Logarithm, and Exponentiation for common function families.

Applications

• Derivative studies local change in functions.
• Integral studies accumulated output.
• Velocity is the derivative of position as a function of time.

Parent: Fundamental index and Maths MOC.

Study path

Read Domain and Codomain and range before inverse functions. Most mistakes about inverses, graphs, and solving equations come from silently changing one of those sets. Then use the injective/surjective/bijective notes as a quick diagnostic checklist.