Set theory - Equality

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Language - Equality in set theory

The equality relationship indicates that two sets are equal if they contain exactly the same elements. (There is no order among elements of a set.)

Notation

Two sets are equal if they contain exactly the same elements. (There is no order among elements of a set.) <MATH>\Large A = B</MATH>

Proof

A convenient way to prove that A and B are equal is to prove that each is a subset of the other. The proof often consists of two parts:

  1. a proof that A subset B (ie A subset B) and
  2. a proof that B subset A (ie B subset A)

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