Mathematics

The Mathematial Subject Set Theory Including Intersection and Union



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Set theory in mathematics uses Venn diagrams to explain concepts like intersection, union, etc. of sets. Modern set theory was discovered by Georg Cantor and Richard Dedekind in the 1870s.  

Sets are labeled A, B, C, D, etc. Numbers are most commonly used in set theory, but symbols can be used too. The members of a set are all the numbers in that set. For example, if set A is (1, 2, 3, 4), then the members are 1, 2, 3, and 4.

Set A is a subset of set B if all the members of set A are members of set B. For example if set A is (1, 2, 5, 9) and set B is (1, 2, 3, 4, 5, 9, 10), then set A is a subset of set B because the numbers 1, 2, 5, 9 are also in set B.

The intersection of set A and set B is the members that set A and set B have in common. For example, if set A equals (1, 2, 6, 10, 15, 17) and set B equals (1, 5, 7, 10, 20, 30), then the intersection of set A and set B is (1,10). The union of set A and set B is similar to the intersection. The union of set A and set B is all the members included in both sets. For example, if set A equals (1, 2, 3, 4, 19, 30, 59,60) and set B equals (9, 30, 70, 100), then the union of set A and set B is the set (1, 2, 3, 4, 9, 19, 30, 59, 60, 70, 100).

The set difference of set A and set B is the members of set A that are not in set B. Conversely, the members of set B that are not in set A is the set difference of set B and set A. For example, if set A is (1, 2, 6, 10, 2000) and set B is (1, 2, 10, 100), then the set difference of set A and set B is (6, 2000) and the set difference of set B and set A is the set (100).

The symmetric difference is the set difference of the union and intersection. It is, in other words, all the members that are in one of the sets, but not both. For example, if set A is (1, 9, 100, 205, 333) and set B is (1, 200, 333), then the symmetric difference is the set (9, 100, 200, 205).   

A set can have zero members (called the null set), one member, many members, or an infinite number of members (called the infinite set). Set theory is closely connected with mathematical logic.  

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ARTICLE SOURCES AND CITATIONS
  • InfoBoxCallToAction ActionArrowhttp://en.wikipedia.org/wiki/Set_theory
  • InfoBoxCallToAction ActionArrowhttp://plato.stanford.edu/entries/set-theory/
  • InfoBoxCallToAction ActionArrowhttp://mathworld.wolfram.com/SetTheory.html