Difference between revisions of "Set (mathematics)"
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For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. | For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. | ||
| − | Sets are one of the most fundamental concepts in mathematics. | + | Sets are one of the most fundamental concepts in [[mathematics]]. |
| + | |||
| + | == Set theory == | ||
Developed at the end of the 19th century, [[set theory]] is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. | Developed at the end of the 19th century, [[set theory]] is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. | ||
| Line 19: | Line 21: | ||
== See also == | == See also == | ||
| + | * [[Alternative set theory]] | ||
| + | * [[Axiomatic set theory]] | ||
| + | * [[Category of sets]] | ||
| + | * [[Class (set theory)]] | ||
* [[Counting]] | * [[Counting]] | ||
* [[Data set]] | * [[Data set]] | ||
| + | * [[Dense set]] | ||
| + | * [[Family of sets]] | ||
| + | * [[Fuzzy set]] | ||
| + | * [[Georg Cantor]] | ||
* [[Idempotence]] | * [[Idempotence]] | ||
* [[Identification scheme]] | * [[Identification scheme]] | ||
| + | * [[Internal set]] | ||
* [[Mathematical object]] | * [[Mathematical object]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
| + | * [[Mereology]] | ||
| + | * [[Multiset]] | ||
| + | * [[Naive set theory]] | ||
| + | * [[Near sets]] | ||
* [[Permutation]] | * [[Permutation]] | ||
| + | * [[Principia Mathematica]] | ||
| + | * [[Rough set]] | ||
| + | * [[Russell's paradox]] | ||
| + | * [[Sequence (mathematics)]] | ||
| + | * [[Set notation]] | ||
* [[Set theory]] | * [[Set theory]] | ||
* [[Space (mathematics)]] | * [[Space (mathematics)]] | ||
| + | * [[Taxonomy]] | ||
| + | * [[Tuple]] | ||
* [[Universe (mathematics)]] | * [[Universe (mathematics)]] | ||
* [[Unique identifier]] | * [[Unique identifier]] | ||
| + | * [[Venn diagram]] | ||
== External links == | == External links == | ||
| Line 35: | Line 58: | ||
* [https://en.wikipedia.org/wiki/Set_(mathematics) Set (mathematics)] @ Wikipedia | * [https://en.wikipedia.org/wiki/Set_(mathematics) Set (mathematics)] @ Wikipedia | ||
| − | [[Mathematics]] | + | [[Category:Mathematics]] |
| + | [[Category:Set theory]] | ||
Latest revision as of 09:48, 7 September 2016
In mathematics, a set is a collection of distinct mathematical objects, considered as an object in its own right.
Description
For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}.
Sets are one of the most fundamental concepts in mathematics.
Set theory
Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.
Mathematics education
In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.
History
The German word Menge, rendered as "set" in English, was coined by Bernard Bolzano in his work The Paradoxes of the Infinite.
See also
- Alternative set theory
- Axiomatic set theory
- Category of sets
- Class (set theory)
- Counting
- Data set
- Dense set
- Family of sets
- Fuzzy set
- Georg Cantor
- Idempotence
- Identification scheme
- Internal set
- Mathematical object
- Mathematics
- Mereology
- Multiset
- Naive set theory
- Near sets
- Permutation
- Principia Mathematica
- Rough set
- Russell's paradox
- Sequence (mathematics)
- Set notation
- Set theory
- Space (mathematics)
- Taxonomy
- Tuple
- Universe (mathematics)
- Unique identifier
- Venn diagram
External links
- Set (mathematics) @ Wikipedia
