Most recent change of Set

Edit made on April 26, 2013 by ColinWright at 15:09:13

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HEADERS_END
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 EQN:\in\ {red, orange, yellow, green, blue, indigo, violet} EQN:red\in\{~red,~orange,~yellow,~green,~blue,~indigo,~violet\} or Japan EQN:\in\ { x : x is a Country in Asia } 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.

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How many different definitions of the word "Set" can you think of?