1.5: Summary, Cheat Sheet - Sets and Functions

1.5: Summary, Cheat Sheet

IN PROGRESS This chart summarizes all of the notation we’ve introduced throughout the chapter.

Name Description Example
$\{ \}$ set used to define a set $S = \{ 1, 2, 3, 4, … \}$
$\in$ in, element of used to denote that an element is part of a set $1 \in {1, 2, 3}$
$\not \in$ not in, not an element of used to denote than an element is not part of a set $4 \not \in {1, 2, 3}$
$\mid S \mid$ cardinality used to describe the size of a set (refers to the number of unique elements if the set is finite) $S = \{1, 2, 2, 2, 3, 4, 5, 5 \}$
$\mid S \mid = 5$
$:$, $\mid$ such that used to denote a condition, usually in set-builder notation or in a mathematical definition $\{x^2 : x + 3 \text{ is prime}\}$
$\subseteq$ subset set $A$ is a subset of set $B$ when each element in $A$ is also an element in $B$ $A = \{ 1, 2 \}$
$B = \{ 2, 1, 4, 3, 5 \}$
$A \subseteq B$
$\supseteq$ superset set $A$ is a superset of set $B$ when $B$ is a subset of $A$ $A = \{ 2, 4, 6, 7, 8 \}$
$B = \{ 2, 4, 8 \}$
$A \supseteq B$