Notation

The following notations usually differ slightly between texts, so they are clarified here.

Sets and Functions

• $\mathbb N_+ = \lbrace 1, 2, 3, \dots \rbrace$
• $\mathbb N = \lbrace 0, 1, 2, 3, \dots \rbrace$
• $A \subseteq B$ or $A \subset B$: $A$ is a subset of $B$ (includes $A = B$)

• $A \subsetneq B$: $A$ is a strict subset of $B$ ($A \neq B$)

• $f: A \hookrightarrow B$: $f$ is an injective function from $A$ to $B$
• $g: A \twoheadrightarrow B$: $g$ is a surjective function from $A$ to $B$
• $h: A \leftrightarrow B$: $h$ is a bijective function from $A$ to $B$