Set theory index

Set theory is the baseline language for modern maths: it tells us what objects exist, how they are grouped, and how structures are built from them. Most later definitions quietly depend on set language.

Local notes

• Set — collections, elements, subsets, and operations.
• Number sets — standard sets such as $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, and $\mathbb{C}$.
• Interval — connected subsets of the real line, used constantly as domains.
• Relation — a subset of a Cartesian product describing connections between objects.
• Mapping — an assignment from one set to another.
• Injective function, Surjective function, Bijective function — important mapping properties.
• Set theory Key concepts, Set theory Equations and definitions, Set theory Examples, Set theory Common pitfalls.

Why it matters

Set theory prevents vague statements. Instead of saying “the function works for numbers”, say $f:\mathbb{R}\setminus \{0\}\to \mathbb{R}$ or $f:[0,\infty )\to [0,\infty )$. That difference decides whether inverses, derivatives, and physical interpretations are valid.

Parent map: Maths MOC.

Study path

Start with Set and Number sets, then read Interval for real-line notation. After that, Relation and Mapping explain why functions are defined the way they are. The mapping-property notes are best read after Function.