Sets

A set is a mathematical object with a notion of membership i.e. whether something is in it or not.

Since they do NOT have a notion of counting, you can only include an element once.
That is, $\{A,B,C\}=\{A,A,B,C\}=\{A,B,B,C,C\}$.
(sets are typically wrapped in curly braces $\{\}$)

We can interact with a set $S$ by asking whether an element $a$ is in the set (with $a\in S$), and asking how many (unique) elements are in the set ($|S|$).

• For example, let $A=\{1,banana,⭐\}$
• $1\in A$? True.
• $2\in A$? False.
• $|A|=3$.
• $|\{1,1,2,2,3,4\}|=4$.

There are also useful operations between sets

Some common (and useful) examples of (non-finite) sets:

• the natural numbers $\mathbb{N}$
• the integers $\mathbb{Z}$
• the