Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
sav08:lattices [2010/04/08 11:00] vkuncak |
sav08:lattices [2011/05/03 16:46] vkuncak |
||
|---|---|---|---|
| Line 3: | Line 3: | ||
| **Definition:** A lattice is a [[:Partial order]] in which every two-element set has a least upper bound and a greatest lower bound. | **Definition:** A lattice is a [[:Partial order]] in which every two-element set has a least upper bound and a greatest lower bound. | ||
| - | **Lemma:** In a lattice every non-empty set has a lub ($\sqcup$) and glb ($\sqcap$). | + | **Lemma:** In a lattice every non-empty finite set has a lub ($\sqcup$) and glb ($\sqcap$). |
| **Proof:** is by ++| **induction!** ++ \\ | **Proof:** is by ++| **induction!** ++ \\ | ||