2026-01-12
An unordered collection of unique elements.
eg. \(\{ 1, 2, 3 \}\)
^ Set-Roster Notation
Let \(A\) be a set
\(x \in A\) means \(x\) is in the set \(A\)
\(x \notin A\) means \(x\) is not in the set \(A\)
\(A \subseteq B\) means \(A\) is a subset of \(B\)
\(A \subset B\) or \(A \subsetneq B\) means \(A\) is a proper subset of \(A\)
\(\mathbb{R}\) means the set of all real numbers
\(\mathbb{Q}\) means the set of all rational numbers
\(\mathbb{Z}\) means the set of all integers
\(\mathbb{Z}^{+}\) or \(\mathbb{N}\) means the set of all natural numbers
Let \(P(x)\) be some property about \(x\) . The notation \(\{ x \in A \mid P(x) \}\) or \(\{ x \in A \colon P(x) \}\) means the set of all \(x\) in \(A\) such that \(P(x)\) is true.
The cardinality of a set \(A\) , denoted as \(\lvert A \rvert\) (not absolute value) or \(N(A)\) , is the number of elements in \(A\) .
The empty set is a subset of every set.
In sets, order/repeats dont matter. In n-tuples, both of these matter. n-tuples are denoted by parentheses. ordered pairs refer to 2-tuples, and ordered triples refer to 3-tuples.
For sets \(A\) and \(B\) , \(A \times B = \{(a,b) \mid a \in A \text{ and } b \in B \}\)
"The're just words"
Strings consisting of 0's and 1's
made with \(\KaTeX\)