A **set** is a single object that is a collection of other objects called [[Element of a Set|elements]] --- Cantor's Definition: >A **set** is a gathering together into a whole of definite, distinct objects of our perception or our thought—which are called elements of the set. --- ### Notation For each of the following cases, the plain-English version of each example is called the "Semantic Description" #### Finite Roster / Extensional form Where every member of the set is $A #### Infinite Roster / Ostensive form #### Set-Builder / Intensional form $D=\{2n \mid n\in \mathbb{Z}\}$ #### Two sets are [[Equality of sets|equal]] if and only if they have the exactly same elements The set with no elements is called the [[empty set]] A set with one element is called a [[‡ Singleton]]