Discussion Overview
The discussion revolves around the terminology used to describe a collection of items that may include repeated elements, contrasting this with the definition of a set where elements are unique. Participants explore possible terms and clarify the distinctions between sets and other collections.
Discussion Character
Main Points Raised
- One participant notes that by definition, elements in a set must be unique and questions what term could describe a collection with repeated elements, providing an example.
- Another participant suggests the term "multiset" as a suitable descriptor for collections that allow repeated elements.
- A third participant expresses gratitude for the suggestion, indicating it meets their needs.
- Another participant adds that a set is defined by its elements alone, implying that repeated elements do not change the identity of the set, and proposes a notation to distinguish copies of elements.
Areas of Agreement / Disagreement
Participants generally agree on the distinction between sets and collections with repeated elements, but there is no consensus on the notation or terminology beyond "multiset."
Contextual Notes
The discussion highlights the limitations of standard set theory definitions and the need for additional notation to represent repeated elements, which remains unresolved.