Abstract Set

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An abstract set is an abstract entity that can represent zero or more distinct entities (set members).



References

2013

  • (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Set_(mathematics) Retrieved:2013-12-1.
    • In mathematics, a set is a collection of distinct objects, considered as an object in its own right. 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. 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. 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. The term itself was coined by Bolzano in his work The Paradoxes of the Infinite.

2009

  • http://en.wiktionary.org/wiki/set
    • A matching collection of similar things; A collection of various objects for a particular purpose; An object made up of several parts; A well-defined collection of mathematical objects and elements, often having a common property; (informal) Set theory; A group of people, usually meeting ...


  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Set_(category_theory)
    • In mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose morphisms are all functions. ...
  • http://planetmath.org/encyclopedia/Set.html
    • Sets can be of “real” objects or mathematical objects, but the sets themselves are purely conceptual. This is an important point to note: the set of all cows (for example) does not physically exist, even though the cows do. The set is a “gathering” of the cows into one conceptual unit that is not part of physical reality. This makes it easy to see why we can have sets with an infinite number of elements; even though we may not be able to point out infinitely many objects in the real world, we can construct conceptual sets with an infinite number of elements.