+++
title = "Semilattice"
author = "Yann Herklotz"
tags = []
categories = []
backlinks = ["2e1a"]
forwardlinks = []
zettelid = "2e1a1"
+++

-   partially ordered set that has either a join or a meet
-   There are join-semilattice (least upper bound, supremum)
-   There are meet-semilattice (greatest lower bound, infimum)
-   a lattice is both a meet-semilattice and a join-semilattice
-   A set with finite elements is always a lattice, because if we take
    two distinct elements, one will be the least element (join) and the
    other will be most element (meet)