Set
Instance of: mathematical model
AKA: empty set; singleton; infinite set
Distinct from: list
English: A set is a collection of elements with no ordering, e.g. \(\{1,2,3\}=\{3,2,1\}\).
Formalization:
Roster notation \[ A=\{4,2,1,3\} \] Abbreviation with ellipsis \[ A=\{1,2,3,...,1000\} \] Infinite sets beginning and or ending in ellipsis \[ A=\{1,2,3,...\} \]
\[ A=\{...,-3,-2,-1,0,1,2,3,...\} \]
Semantic definition uses a natural language rule to determine which elements belong in a set
Let A be the set whose members are the first four positive integers.
Let B be the set of colors of the French flag.