What a set is
What is a set?
A well-defined collection of objects.
What are the two terms for objects in a set?
What’s the difference between a set and a list?
What’s the symbol for an empty set?
\[\varnothing\]
Membership notation
What does
\[x \in S\]
mean?
$x$ is a member of the set $S$.
What does
\[x \notin S\]
mean?
$x$ is not a member of the set $S$.
Set comprehension
How could you write the set of even natural numbers using set comprehension?
\[\\{ x \vert x \in \mathbb{N} \wedge x \,\text{is even} \\}\]
What would the compact form of
\[\{ x \vert x \in \mathbb{N} \wedge $x$ \,\text{is even} \}\]
be?
\[\\{ x \in \mathbb{N} \vert x \,\text{is even} \\}\]
What set does
\[\{10^n \vert n \le 1\}\]
describe?
\[\\{ 10, 100, 1000, 10000 \\}\]
How would you describe the set $\{ 5, 10, 15, ...\}$?
\[\\{ x \vert x \in N \wedge x \mod 5 = 0 \\}\]
Set difference
What does $A \\ B$ mean?
All the members that are in A but not in B.
What is the $A \\ B$ operator called?
What does the Venn diagram for $A \\ B$ look like?
Subsets
What does it mean for $A$ to be a subset of $B$?
Every member of $A$ is also a member of $B$.
What is the notation for $A$ being a subset of $B$?
\[A \subseteq B\]
What is the notation for $A$ being a proper subset of $B$?
\[A \subset B\]
What’s the difference between a subset and a proper subset?
A proper subset means $A$ is a subset of $B$ and they are not equal.
Cartesian product
What is the Cartesian product of two sets $A$ and $B$?
The set of all ordered pairs $(a, b)$ such that $a \in A$ and $b \in B$.
What is the set comprehension notation for the Cartesian product of $A$ and $B$?
\[A \times B = \\{ (a, b) \vert a \in A \wedge b \in B \\}\]
What is the notation for the Cartesian product of $A$ and $B$?
\[A \times B\]
Cardinality
What is the cardinality of a set?
The number of members in the set.
What is the notation for the cardinality of $A$?
\[ \vert A \vert \]
What is a countably infinite set?
A set whose members can be counted by using the infinite set $\mathbb{N}$.
What is the formula for the cardinality of the Cartesian product of two sets $A$ and $B$?
\[ \vert A \vert \times \vert B \vert \]
