The set of all even integers, expressed in set-builder notation. In set theory and its applications to logic, mathematics, and computer science, set-builder...

description. Set-builder notation specifies a set as a selection from a larger set, determined by a condition on the elements. For example, a set F can be...

ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation, that is A × B = { ( a , b ) ∣ a ∈ A    and    b ∈ B } . {\displaystyle...

has blonde hair} denotes the set of everything with blonde hair. This notation is called set-builder notation (or "set comprehension", particularly in...

2.  Set-builder notation for a singleton set: { x } {\displaystyle \{x\}} denotes the set that has x as a single element. {□, ..., □} Set-builder notation:...

Z notation, a formal notation for specifying objects using Zermelo–Fraenkel set theory and first-order predicate logic Ordinal notation Set-builder notation...

mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions. Consider the following example in mathematical set-builder...

the set of elements which are in A, in B, or in both A and B. In set-builder notation, A ∪ B = { x : x ∈ A  or  x ∈ B } {\displaystyle A\cup B=\{x:x\in...

3 / 2 , {\displaystyle 1.5=3/2,} are two notations for the same number. Similarly, using set builder notation, { x ∣ x ∈ Z  and  0 < x ≤ 3 } = { 1 , 2...

of the collection M {\displaystyle M} is defined as the set (see set-builder notation) ⋂ A ∈ M A = { x :  for all  A ∈ M , x ∈ A } . {\displaystyle \bigcap...

the notation 2S denoting the power set P(S) are demonstrated in the below. An indicator function or a characteristic function of a subset A of a set S with...

the empty set, but this is now considered to be an improper use of notation. The symbol ∅ is available at Unicode point U+2205 ∅ EMPTY SET. It can be...

using the XOR operation ⊕ on the predicates describing the two sets in set-builder notation: A Δ B = { x : ( x ∈ A ) ⊕ ( x ∈ B ) } . {\displaystyle A\mathbin...

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...

mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related...

notations are described in International standard ISO 31-11. Thus, in set builder notation, ( a , b ) = ] a , b [ = { x ∈ R ∣ a < x < b } , [ a , b ) = [ a...

expressed notationally as 3 ∈ A {\displaystyle 3\in A} . Writing A = { 1 , 2 , 3 , 4 } {\displaystyle A=\{1,2,3,4\}} means that the elements of the set A are...

this notation is ambiguous, as in some contexts (for example, Minkowski set operations in functional analysis) it can be interpreted as the set of all...

concept of a relation, but using more notation (including set-builder notation): A function is formed by three sets, the domain X , {\displaystyle X,} the...

{\displaystyle A} , to just A {\displaystyle A} set-builder notation: { x | x < 2 } {\displaystyle \{x|x<2\}} , read "the set of x such that x is less than two"....

I is some, possibly countably or uncountably infinite, indexing set. In set notation, De Morgan's laws can be remembered using the mnemonic "break the...

satisfies Φ {\displaystyle \Phi } may be expressed with the shorthand notation Φ ( x ) = y {\displaystyle \Phi (x)=y} . Another approach is taken by the...

(x)} . By the axiom of extensionality this set is unique. We usually denote this set using set-builder notation as S = { x ∈ A | φ ( x ) } {\displaystyle...

steps of collection of sets, followed by a restriction through separation. All results are also expressed using set builder notation. Firstly, given b {\displaystyle...

Set-builder notation Set-theoretic topology Simple theorems in the algebra of sets Subset Θ (set theory) Tree (descriptive set theory) Tree (set theory)...

{\displaystyle k} -subsets of an n {\displaystyle n} -element set. In set theory, the notation [ A ] k {\displaystyle [A]^{k}} is also common, especially...

analysis. Set theory begins with a fundamental binary relation between an object o and a set A. If o is a member (or element) of A, the notation o ∈ A is...

a singleton (also known as a unit set or one-point set) is a set with exactly one element. For example, the set { 0 } {\displaystyle \{0\}} is a singleton...

mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle...

mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...