01.3 Equality, Identity, and Equivalence
1.3 Equality, Identity, and Equivalence Mathematics depends on precise notions of sameness. The symbol = appears simple, but it carries different meanings depending on context. This section separates three levels: equality, identity, and equivalence. Equality is the strictest notion. Two objects are equal if they are the same object in the underlying system. a = b In set theory, equality is extensional. Two sets are equal when they have exactly...