# 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.

Set-builder notation