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The word "set" is the word in English with the most definitions. In Mathematics a set is a collection of well defined and distinct objects. Sets can be indicated by listing the objects e.g. {red, orange, yellow, green, blue, indigo, violet} or by specifying a property e.g. { x : x is a Country in Asia } Sets are a very important idea in Mathematics. Objects in a set are called elements. We write EQN:red\in\{~red,~orange,~yellow,~green,~blue,~indigo,~violet\} or EQN:Japan\in\{x:~x~is~a~country~in~Asia\} However, this simple definition of a set can lead to problems (see Russell's paradox) so sets have to be defined by a very formal and complicated list of axioms of which the Zermelo–Fraenkel axioms with the axiom of choice are the most commonly used. ---- How many different definitions of the word "Set" can you think of?