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06A12-Meet.tex
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06A12-Meet.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{Meet}
\pmcreated{2013-03-22 12:27:37}
\pmmodified{2013-03-22 12:27:37}
\pmowner{yark}{2760}
\pmmodifier{yark}{2760}
\pmtitle{meet}
\pmrecord{10}{32610}
\pmprivacy{1}
\pmauthor{yark}{2760}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{06A12}
\pmsynonym{and operator}{Meet}
\pmrelated{Join}
\pmrelated{Semilattice}
\pmdefines{meet-semilattice}
\pmdefines{meet semilattice}
\pmdefines{lower semilattice}
\endmetadata
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\begin{document}
Certain posets $X$ have a binary operation \emph{meet} denoted by $\land$, such that $x \land y$ is the greatest lower bound of $x$ and $y$. Such posets are called \emph{meet-semilattices}, or \emph{$\land$-semilattices}, or \emph{lower semilattices}.
If $m$ and $m'$ are both meets of $x$ and $y$, then $m \leq m'$ and $m \geq m'$, and so $m = m'$; thus a meet, if it exists, is unique. The meet is also known as the \emph{and operator}.
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\end{document}