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 $red\in\{~red,~orange,~yellow,~green,~blue,~indigo,~violet\}$ or $Japan\in\{x:~x~is~a~country~in~Asia\}$

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?

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