Difference between a boolean algebra and a complete lattice?

luizgguidi · Mar 5, 2009

What is the difference between a boolean algebra and a complete lattice? What are their similarities?

de_brook · Mar 7, 2009

luizgguidi said:

What is the difference between a boolean algebra and a complete lattice? What are their similarities?

a boolean algebra is a complemented distributive lattice. a boolean algebra is a complete lattice. A complemented lattice is one with 'zero element 0 and identity element 1'
while a complete lattice is a lattice in which every chain has a minimum and a maximum elements.
for example, the powerset of an arbitrary non emptyset V is a boolean algebra with minimum element(zero element 0 ) as empty set and maximum element(identity element 1) as V

Difference between a boolean algebra and a complete lattice?

Graduate Expected numbers of cards of a last color remaining

Undergrad The problem of points

Graduate Probability puzzle

Undergrad The countability paradox of computable numbers

Undergrad How does axiom of foundation prevent infinite sequence of elements?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Difference between a boolean algebra and a complete lattice?

Similar threads