| 释义 |
lattice (set theory) A partially ordered set X in which every pair of elements x,y has a least upper bound x ∨ y and a greatest lower bound x ∧ y. The lattice is complete if every subset of X has a least upper bound and greatest lower bound. A power set with ∨ = ∪ and ∧ = ∩ is a complete lattice. ℕ with ≤ = | (divides), ∨ = lcm, and ∧ = hcf is an incomplete lattice as the elements of ℕ have no upper bound.
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