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\)
Subsection 0.1.1 Sets
We give basic terminology and notation for sets. We cover sets in more detail in
Section 2.1 .
A
set is an unordered collection of objects, called
elements or
members of the set. We write
\(b \in A\) when
\(b\) is an element of the set
\(A\text{.}\) We read
\(b \in A\) as “
\(b\) is an element of
\(A\) ” or “
\(b\) is in
\(A\) ”.
Sets can be specified in
roster form by listing the elements explicitly between braces. For example,
\(\set{1, 2, 7}\) is the set containing
\(1\text{,}\) \(2\text{,}\) and
\(7\text{.}\)
To indicate that the list of elements continues in a pattern that can be deduced from the preceding list of elements we use ellipsis (\(\ldots\) ). For example, we have
\begin{equation*}
\set{1, 2, 3,\dots, 10}=\set{1,2,3,4,5,6,7,8,9,10}\text{.}
\end{equation*}
