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2. Relation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Relation_(mathematics)

   [5] [6] Since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, leading to the algebra of sets. Furthermore, the calculus of relations includes the operations of taking the converse and composing relations. [7] [8] [9]

3. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

4. Natural number - Wikipedia

   en.wikipedia.org/wiki/Natural_number

   The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω.

5. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).

6. List of types of numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_types_of_numbers

   Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

7. Element (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Element_(mathematics)

   The number of elements in a particular set is a property known as cardinality; informally, this is the size of a set. [5] In the above examples, the cardinality of the set A is 4, while the cardinality of set B and set C are both 3.

8. Set-theoretic definition of natural numbers - Wikipedia

   en.wikipedia.org/wiki/Set-theoretic_definition...

   The set N of natural numbers is defined in this system as the smallest set containing 0 and closed under the successor function S defined by S(n) = n ∪ {n}. The structure N, 0, S is a model of the Peano axioms (Goldrei 1996). The existence of the set N is equivalent to the axiom of infinity in ZF set theory.

9. Intersection (set theory) - Wikipedia

   en.wikipedia.org/wiki/Intersection_(set_theory)

   Download as PDF; Printable version; In other projects ... The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of odd ...