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  1. Sets

    Writing means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example , are subsets
    Sets … See more

    Notation and terminology

    The binary relation "is an element of", also called set membership, is denoted by the symbol "∈". Writing
    means that "x is an element of A". Equivalent expressions are "x is a member of A", "x bel… See more

    Examples

    Using the sets defined above, namely A = {1, 2, 3, 4}, B = {1, 2, {3, 4}} and C = {red, green, blue}, the following statements are true:
    • 2 ∈ A
    • 5 ∉ A… See more

    Cardinality of sets

    The number of elements in a particular set is a property known as cardinality; informally, this is the size of a set. In the above examples, the cardinality of the set A is 4, while the cardinality of set B and set C are both 3. … See more

    Formal relation

    As a relation, set membership must have a domain and a range. Conventionally the domain is called the universe denoted U. The range is the set of subsets of U called the power set of U and denoted P(U). Thus the relation is … See more

    Further reading

    Halmos, Paul R. (1974) [1960], Naive Set Theory, Undergraduate Texts in Mathematics (Hardcover ed.), NY: Springer-Verlag, ISBN 0-387-90092-6 - "Naive" means that it is not fully axiomatized, not that it is silly or eas… See more

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