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.)

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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 <m>A subset B</m>

   (ie A subset B) and

2. a proof that <m>B subset A</m>

   (ie B subset A)