In Tao's Analysis I, the equality of sets is classified as an axiom rather than a definition.

Why is this not a Definition, but is instead an Axiom .. in Tao Analysis I? "" Axiom 3.2 (Equality of sets). Two sets A and B are equal, A= B, iff every element of A is an element of B and vice versa. "" --- I'm a newbie still becoming familiar with the lingo. In my mind a Definition usually provides a shorthand name for something in terms of previously known concepts. This Axiom 3.2 defines the shorthand "equality" for sets. In contrast Axiom 3.1 says sets are objects (and therefore may be elements of other sets). That to me is an axiom, not a definition. -- Update - apparently a previous edition of the book had this Axiom as a Definition, so the author must have consciously changed it ... intriguing... #maths #settheory

Why is this not a Definition, but is instead an Axiom .. in Tao Analysis I? "" Axiom 3.2 (Equality of sets). Two sets A and B are equal, A= B, iff every element of A is an element of B and vice versa. "" --- I'm a newbie still becoming familiar with the lingo. In my mind a Definition usually provides a shorthand name for something in terms of previously known concepts. This Axiom 3.2 defines the shorthand "equality" for sets. In contrast Axiom 3.1 says sets are objects (and therefore may be elements of other sets). That to me is an axiom, not a definition. #maths #settheory