① Foundations

§1. Set theory¶

Sets¶

Binary relations¶

TBD

Functions¶

TBD

Correspondences¶

TBD

Cardinality and countability¶

TBD

§2. Order theory¶

Order relations¶

Let \(\succeq\) be a binary relation on a nonempty set \(S\). If \(\succeq\) is reflexive and transitive, then \(\succeq\) is called a preorder on \(S\). The pair \((S, \succeq)\) is called a preordered set.

Let \(\succeq\) be a binary relation on a nonempty set \(S\). If \(\succeq\) is reflexive, transitive, and antisymmetric, then \(\succeq\) is called a partial order on \(S\). The pair \((S, \succeq)\) is called a partially ordered set, or poset.

TBD

Joins and meets¶

TBD

Lattices¶

TBD

§3. Number systems¶

\(\mathbb{N}\) Natural numbers¶

\(\mathbb{Z}\) Integers¶

\(\mathbb{Q}\) Rational numbers¶

\(\mathbb{R}\) Real numbers¶

\(\mathbb{C}\) Complex numbers¶

References¶

TBD