Computing - Sets
2021-01-07
What is a set?
A well-defined collection of objects.
What are the two terms for objects in a set?
- Members
- Elements
What’s the difference between a set and a list?
Sets are unordered.
What’s the symbol for an empty set?
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 $S$.
How could you write the set of even natural numbers using set comprehension?
What would the compact form of
\[\{ x \vert x \in \mathbb{N} \wedge $x$ \,\text{is even} \}\]
be?
What set does
\[\{10^n \vert n \le 1\}\]
describe?
How would you describe the set ${ 5, 10, 15, …}$?
What does $A \ B$ mean?
All the members that are in A but not in B.
What is the $A \ B$ operator called?
Difference.
What does the Venn diagram for $A \ B$ look like?
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 $B$?
What is the notation for $A$ being a proper subset of $B$?
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.
What is the Cartesian product of two sets $A$ and $B$?
The set of all ordered pairs $(a, b)$ such thta $a \in A$ and $b \in B$.
What is the set comprehension notation for the Cartesian product of $A$ and $B$?
What is the notation for the Cartesian product of $A$ and $B$?
What is the cardinality of a set?
The number of members in the set.
What is the notation for the carinality of $A$?
What is a countably infinite set?
A set whose members can be counted by using the infinite set $\mathbb{N}$.