Set is a collection of elements where their order and recurrence does not matter. It could be specified using either 202204281704# or 202204281700#. Due to the properties of set, the set \(\{a, b, c\}\) is same with \(\{b, a, c\}\) and \(\{a, a, b, c, c, c\}\), which could be denoted as \(\{a, b, c\} \equiv \{b, a, c\} \equiv \{a, a, b, c, c, c\}\).
Note: There is a fundamental difference between an element \(e\) and a set that contains only that element \(\{e\}\). (\(e \not = \{e\}\))
If there are too many numbers to express, we can abbreviate them using ellipsis (read “and so forth”) as \(\{1,2,3 \cdots 100\}\). There are some 202204281506# that have their own special symbols.
From the set \(S\), we could see that element \(a\) is an element of \(S\). This could be expressed using \(a \in S\). Let’s say we have an element \(d\), but we know that \(d\) is not an element of \(S\), we can denote it as \(d \not \in S\).
Relations
Sets can have various relations with each other. See the following: