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  2. Set (mathematics) - Wikipedia

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

    In set-builder notation, = {:}. The complement may also be called the absolute complement to distinguish it from the relative complement below. Example: If the universal set is taken to be the set of integers, then the complement of the set of even integers is the set of odd integers.

  3. Set-builder notation - Wikipedia

    en.wikipedia.org/wiki/Set-builder_notation

    Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...

  4. List of set identities and relations - Wikipedia

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

    Universe set and complement notation The notation L ∁ = def X ∖ L . {\displaystyle L^{\complement }~{\stackrel {\scriptscriptstyle {\text{def}}}{=}}~X\setminus L.} may be used if L {\displaystyle L} is a subset of some set X {\displaystyle X} that is understood (say from context, or because it is clearly stated what the superset X ...

  5. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    Functional notation: if the first is the name (symbol) of a function, denotes the value of the function applied to the expression between the parentheses; for example, (), ⁡ (+). In the case of a multivariate function , the parentheses contain several expressions separated by commas, such as f ( x , y ) {\displaystyle f(x,y)} .

  6. Naive set theory - Wikipedia

    en.wikipedia.org/wiki/Naive_set_theory

    This notation is called set-builder notation (or "set comprehension", particularly in the context of Functional programming). Some variants of set builder notation are: {x ∈ A | P(x)} denotes the set of all x that are already members of A such that the condition P holds for x. For example, if Z is the set of integers, then {x ∈ Z | x is ...

  7. Union (set theory) - Wikipedia

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

    The last of these notations refers to the union of the collection {:}, where I is an index set and is a set for every ⁠ ⁠. In the case that the index set I is the set of natural numbers , one uses the notation ⋃ i = 1 ∞ A i {\textstyle \bigcup _{i=1}^{\infty }A_{i}} , which is analogous to that of the infinite sums in series.

  8. Element (mathematics) - Wikipedia

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

    In the above examples, the cardinality of the set A is 4, while the cardinality of set B and set C are both 3. An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements. The above examples are examples of finite sets.

  9. Intersection (set theory) - Wikipedia

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

    This last example, an intersection of countably many sets, is actually very common; for an example, ... is defined as the set (see set-builder notation) ...