Collection
Elementary
A collection is a group of objects considered together.
Graduate (set theory)
Collection is an informal word, used as a synonym for “set,” to produced for variety (e.g., “a collection of subsets”) or for classes that are too large to be sets (“the collection of all sets”).
Examples
Examples
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$\setdef{1, 2, 2}$
Elementary
$\setdef{1, 2, 2}$ is a collection, and as a set it equals $\setdef{1, 2}$, with two elements.
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The class of all sets
Graduate
The class of all sets is a collection.
Distinctions involving this term
- Types of collections: Mathematics has several kinds of “a bunch of things,” which differ in whether order and repetition matter. A set ignores order and repetition. A multiset keeps repetition. A sequence keeps order and repetition. “Collection” is informal, and “group” is a technical term for a set with an operation.