About: What are some examples of a set

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Sets are collections of arbitrary objects, considered as an object in its own right, e.g. * your family (a collection of all you relatives) * a book (as a collection of sheets) * me and you ("us") it's not even necessary for the set to be a particular meaningfull collection, nor to contain any object at all: are all perfect sets. The things that make up a set are said to be its "elements". So, * your father is an element of your family * i am an element of us * the sun is an element of me, you, the number 1 and the stars ('cause the sun itself is a star) example

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rdfs:label	What are some examples of a set
rdfs:comment	Sets are collections of arbitrary objects, considered as an object in its own right, e.g. * your family (a collection of all you relatives) * a book (as a collection of sheets) * me and you ("us") it's not even necessary for the set to be a particular meaningfull collection, nor to contain any object at all: are all perfect sets. The things that make up a set are said to be its "elements". So, * your father is an element of your family * i am an element of us * the sun is an element of me, you, the number 1 and the stars ('cause the sun itself is a star) example
dcterms:subject	Answered questions Math
abstract	Sets are collections of arbitrary objects, considered as an object in its own right, e.g. * your family (a collection of all you relatives) * a book (as a collection of sheets) * me and you ("us") it's not even necessary for the set to be a particular meaningfull collection, nor to contain any object at all: * the collection summer and your telephone * the collection of me, you, the number 1 and the stars * the collection of the thought you had when you got up this morning * the collection of nothing (that's called the empty set of which there is only one in the whole universe, the empty set) are all perfect sets. Only thing is: Sets must be described unambiguously, that is: it must be possible, for any thinkable object, to tell whether it is or is not part of the set. Accordingly, "the good" can hardly be a set, for it is not easy to tell whether somebody is good or bad (if any). The things that make up a set are said to be its "elements". So, * your father is an element of your family * i am an element of us * the sun is an element of me, you, the number 1 and the stars ('cause the sun itself is a star) Mathematicians always seek short ways to write down things. They would write: * { summer, your telephone } * { the thought you had when you got up this morning } * the empty set: ∅ * another way to write down the empty set: {} * { 1, 2, ..., 10 } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} * { a, b, c, ..., h, i, j } = { a, b, c, d, e, f, g, h, i, j} The fact that a particular object is or is not an element of a set is symbolized: * a ∈ S, if a is element of the set S * a ∉ S, if a is not element of the set S example * 1 ∈ {1,2} * 1 ∉ ∅ Sets which have plenty of elements, or whose natural language description would be really awkward can be mathematically described: * { x : x is a star } (speak: the set of all x such that x is a sun) * { any mutual friend of x and y : x is chinese and y is american } -- that's all the people of the world who have both a chinese and an american as a friend * { x * 0.5: x ∈ {1,2,10} or x < -3 }

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