Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Equivalence of Sets

The following definition is adapted from the article Set Theory in the macropedia of the Encyclopedia Britannica (1992):

The set S is defined as equivalent to the set T, symbolized

if and only if there exists a third set the members of which are ordered pairs such that:

  1. the first member of each pair is an element (or member) of S and the second is an element of T, and
  2. each member of S occurs as a first member and each member of T occurs as the second member of exactly one pair.

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