Definition
A set is a well defined collection of objects. Georg Cantor, the founder of set theory, gave the following definition of a set at the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre:
A set is a gathering together into a whole of definite, distinct objects of our perception and of our thought – which are called elements of the set.The elements or members of a set can be anything: numbers, people, letters of the alphabet, other sets, and so on. Sets are conventionally denoted with capital letters. Sets A and B are equal if and only if they have precisely the same elements.
As discussed below, the definition given above turned out to be inadequate for formal mathematics; instead, the notion of a "set" is taken as an undefined primitive in axiomatic set theory, and its properties are defined by the Zermelo–Fraenkel axioms. The most basic properties are that a set "has" elements, and that two sets are equal (one and the same) if and only if every element of one is an element of the other.
Read more about this topic: Set (mathematics)
Famous quotes containing the word definition:
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
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—Florence Nightingale (1820–1910)
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—George Eliot [Mary Ann (or Marian)