Lattice theory

Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.Complements need not be unique. A relatively complemented lattice is a lattice such that every interval [c, d], viewed as a bounded lattice in its own right, is a complemented lattice. An orthocomplementation on a complemented lattice is an involution that is order-reversing and maps each element to a complement. An orthocomplemented lattice satisfying a weak form of the modular law is called an orthomodular lattice. In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra. (Wikipedia).

Complemented lattice
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From playlist Algebra 1

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From playlist Multiplication and Division of Whole Numbers

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From playlist Set Theory

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From playlist Set Theory

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From playlist QTS Numeracy Skills

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We're busy people who learn to code, then practice by building projects for nonprofits. Learn Full-stack JavaScript, build a portfolio, and get great references with our open source community. Join our community at https://freecodecamp.com Follow us on twitter: https://twitter.com/freecod

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Related pages

Quantum logic | Linear subspace | Vector space | Separable space | Modular lattice | Lattice (order) | Distributive lattice | Pseudocomplemented lattice | John von Neumann | Mathematics | De Morgan's laws | Involution (mathematics) | Closed set | Intersection | Order theory | Hilbert space | Inner product space | Garrett Birkhoff | Orthogonal complement | Boolean algebra (structure)