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 $|A|$.

Describing Sets

There are 2 ways to describe sets.

Relationship Between Sets

Interesting properties:

$\emptyset \subseteq A$ for all set $A$.

$\emptyset \subset A$ for all set $A \neq \emptyset$.

Set Operations

Arbitrary Number of Operations