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Set theory
A set, in mathematics, is a collection of distinct entities, called its elements, considered as a whole. The early study of sets led to a family of paradoxes and apparent contradictions. It therefore became necessary to abandon "naïve" conceptions of sets, and a precise definition that avoids the paradoxes turns out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this article:
- A = the set of the numbers 1, 2 and 3.
- B = the set of primary light colors -- red, green and blue.
- C = the empty set (the set with no elements).
- D = the set of all books in the British Library.
- E = the set of all positive integers, 1, 2, 3, 4, and so on.
Note that the last of these sets is infinite.
A set is the collection of its elements considered as a single, abstract entity. Note that this is different from the elements themselves, and may have different properties. For example, the elements of D are flammable (they are books), but D itself is not flammable, since abstract objects cannot be burnt. .... (read more)
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