Characteristic function

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Revision as of 14:15, 7 December 2008 by imported>Richard Pinch (added elementary operations)
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In set theory, the characteristic function or indicator function of a subset A of a set X is the function, often denoted χA or IA, from X to the set {0,1} which takes the value 1 on elements of A and 0 otherwise.

We can express elementary set-theoretic operations in terms of characteristic functions:

  • Empty set:
  • Intersection:
  • Union:
  • Symmetric difference: