1 Elementary Set Theory Notation: fgenclose a set. f1;2;3g= f3;2;2;1;3gbecause a set is not de ned by order or multiplicity. f0;2;4;g= fxjxis an even natural numbergbecause two ways of writing. Basic vocabulary used in set theory A set is a collection of distinct objects. The objects can be called elements or members of the set. A set does not list an element more than once since an element is either a member of the set or it is not. There are three main ways to identify a set: 1. A written description 2. List or Roster method 3. In the so-called naive set theory, which is sufficient for the purpose of studying abstract algebra, the notion of a set is not rigorously defined. We describe a set as a well-defined aggregation of objects, which are referred to as members or elements of the set. If a certain object is an element of a set, it is said to be contained in that set. what a set is, we will describe what can be done with sets. Intuitivelly, a set is a collection of objects of any kind, which we call the elements of a set. The second primitive notion of set theory is the notion of belonging. We write x ∈ X meaning ‘x belongs to the set X’, or ‘x is an element of X’ (Tipically.

Set Theory Basic deﬁnitions and notation A set is a collection of objects. For example, a deck of cards, every student enrolled in Math , the collection of all even integers, these are all examples of sets of things. Each object in a set is an element of that set. The two of diamonds is an element of the set. As we have already discussed, in mathematics set theory, a set is a collection for different types of objects and collectively itself is called an object. For example, number 8, 10, 15, 24 are 4 distinct numbers, but when we put them together, they form a set of 4 . DEFINING A SET A set is a collection of well defined entities, objects or elements. OR A set is a group of one or more elements with common characteristics. OR A set is a collection of distinct, unordered objects. Sets are typically collection of numbers. So, a set may contain any type of data (including other sets). 4. A set is an unordered collection of objects, and as such a set is determined by the objects it contains. Before the 19th century it was uncommon to think of of set theory were a real threat to the security of the foundations. But with The notes are self-contained. The more set-theory ori-ented books below are those of Devlin, Nissanke.

The algebra of sets, like the algebra of logic, is Boolean algebra. When George Boole wrote his book about logic, it was really as much about set theory as logic. In fact, Boole did not make a clear distinction between a predicate and the set of objects for which that predicate is true. His algebraic laws and formulas apply equally to both. Set theory - Set theory - Axioms for compounding sets: Although the axiom schema of separation has a constructive quality, further means of constructing sets from existing sets must be introduced if some of the desirable features of Cantorian set theory are to be established. Three axioms in the table—axiom of pairing, axiom of union, and axiom of power set—are of . sets. Informal set theory begins with an existing domain of objects, presumed not to be sets, and constructs all sets over that domain. For example, one can construct sets over the domain of natural numbers, or over the domain of persons, or whatever. By contrast, pure set theory assumes no pre-existing domain, but.