In mathematics, two sets are almost disjoint[1][2] if their intersection is small in some sense; different definitions of "small" will result in different definitions of "almost disjoint".
^Kunen, K. (1980), "Set Theory; an introduction to independence proofs", North Holland, p. 47
^Jech, R. (2006) "Set Theory (the third millennium edition, revised and expanded)", Springer, p. 118
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are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjointsets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A...
In mathematics, two sets are almostdisjoint if their intersection is small in some sense; different definitions of "small" will result in different definitions...
In mathematics, the disjoint union (or discriminated union) A ⊔ B {\displaystyle A\sqcup B} of the sets A and B is the set formed from the elements of...
In mathematics, fuzzy sets (also known as uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently...
set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set...
notation was utilized in definitions; for example, Cantor defined two sets as being disjoint if their intersection has an absence of points; however, it is debatable...
relate sets as well. A derived binary relation between two sets is the subset relation, also called set inclusion. If all the members of set A are also...
closed under complements and countable disjoint unions π-system – Family of sets closed under intersection Ring of sets – Family closed under unions and relative...
concerns the impossibility of a set of sets, whose members are all sets that do not contain themselves. If such a set could exist, it could neither contain...
still disjoint from x {\displaystyle x} because we are using the same element relation and no new sets were added. Axiom of extensionality: Two sets are...
symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection...
set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets...
10), ..., (♣, 6), (♣, 5), (♣, 4), (♣, 3), (♣, 2)}. These two sets are distinct, even disjoint, but there is a natural bijection between them, under which...
compactness in terms of closed sets; this is its most prominent application. Other applications include proving that certain perfect sets are uncountable, and the...
between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships...
a maximum disjointset (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping...
numbers and the interval [ 0 , 1 ] {\displaystyle [0,1]} . If A and B are disjointsets, then | A ∪ B | = | A | + | B | . {\displaystyle \left\vert A\cup B\right\vert...
sequence of pairwise disjointsets. Algebra of sets – Identities and relationships involving sets Complement (set theory) – Set of the elements not in...
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