Notes taken for CSCB36 course at UofT, this post is for Chapter 0, mainly talks about sets and fundamental mathematical units.
Sets
If an object is $a$ in $A$, then we write $a \in A$, if not, we write $a \notin A$.
If a set has 0 elements, we call that an empty set, or $\emptyset$.
Number of elements within a set $A$ is called its size or cardinality, denoted by $A$.
 For infinite set $A$, $A = \infty$
 For empty set $\emptyset$, $\emptyset = 0$
Describing Sets
There are 2 ways to describe sets.
 Extensional: List all elements within a set. For example $\{1,2,3\}$.
 Intensional: Describle the set with format $\{x: \text{x is odd number}\}$.
Relationship Between Sets
 $A \subseteq B$: If every element in $A$ is also in $B$, then $A$ is a subset of $B$.
 $B \supseteq A$: If $A \subseteq B$ then this holds.
 $A \subseteq B$ and $B \subseteq A$ then $A = B$.
 $A \subseteq B$ and $A \neq B$ then $A$ is a proper subset of $B$, or $A \subset B$.
 $B \supset A$ if $A \subset B$.
Interesting properties:
$\emptyset \subseteq A$ for all set $A$.
$\emptyset \subset A$ for all set $A \neq \emptyset$.
Set Operations

Union of $A$ and $B$ or $A \cup B$, is the set of elements that belongs to $A$ or $B$.

Intersection of $A$ and $B$ or $A \cap B$, is the set of element that belongs to $A$ and $B$. If $A \cap B = \emptyset$, then $A$ and $B$ are disjoint.

Difference of $A$ and $B$ or $A  B$, is the set of elements that belong to $A$ but not to $B$.