set theory

Basic idea

Foundation of modern math: everything is built from sets and membership ($\in$). Relations and functions are themselves sets of ordered pairs.

Key formulas

• Membership: $x \in A$
• Subset: $A \subseteq B \iff \forall x.\, x\in A \Rightarrow x\in B$
• Union/intersection/difference: $A\cup B$, $A\cap B$, $A\setminus B$
• Cartesian product: $A\times B = \{(a,b) : a\in A, b\in B\}$
• Relation $R$ on $X$: $R \subseteq X\times X$

Pages

• AntiSymmetry
• Reflexivity
• Transivity

Siblings

• Blogs
• calculus
• complex numbers
• linear algebra