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Antichain

💡 Words with a Similar Meaning to "Antichain"

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WordDefinition
chainnounA series of interconnected rings or links usually made of metal.
multichain(chemistry) Of or pertaining to more than one chain.
total ordernoun(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).
lower setnoun(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself.
upper setnoun(mathematics, order theory) A subset of a poset which contains any ascending chain which starts at any element of itself.
well-ordernoun(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.
partial ordering relationnoun(set theory) A partial order.
partially ordered setnoun(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order.
ordernoun(countable) A command.
directed setnoun(algebra, set theory) A set equipped with a preorder such that for any two elements a and b there is an element c such that a ≤ c and b ≤ c.
posetnoun(set theory, order theory) A partially ordered set.
totally ordered setnoun(set theory) A set having a specified total order.
quasiordernoun(set theory) A preorder.
latticenounA flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.
ordered setnoun(mathematics) A totally ordered set.
partial ordernoun(set theory, order theory) (informal) An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); (formal) a binary relation that is reflexive, antisymmetric, and transitive.
proper subsetnoun(set theory) a set that is a subset of the set, but not equal to it.
linear ordernoun(set theory, order theory) total order
set-theoretic differencenoun(set theory, of two sets A and B) The set that contains exactly those elements belonging to A but not to B; the relative complement of B in A.
idealnounA perfect standard of beauty, intellect etc., or a standard of excellence to aim at.

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