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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 ...
List comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
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 ...
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 ...
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 ...
3. In set-builder notation, it is used as a separator meaning "such that"; see { : }. / 1. Denotes division and is read as divided by or over. Often replaced by a horizontal bar. For example, 3 / 2 or . 2. Denotes a quotient structure.
The reason is as follows: The intersection of the collection is defined as the set (see set-builder notation) = {:,}. If M {\displaystyle M} is empty, there are no sets A {\displaystyle A} in M , {\displaystyle M,} so the question becomes "which x {\displaystyle x} 's satisfy the stated condition?"