Notions of Set Theory

Overview

Many of the common notions used in mathematics can be formulated within set theory.

Definitions

• Subset - {% A \subset B %}
• Complement - {% A^c = U / A %}
• Ordered Pair - {% (x,y) = \{\{x\}, \{x,y\}\} %}
• Cartesian Product - {% A \times B = \{(x,y)| x \in A \, and \, y \in B \} %}
• Relation - {% R \subset A \times B %}
  • Equivalence Relation
• Function - {% \forall x \in A, \exists ! y \; s.t. \, (x,y) \in R %}