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  text: '[summary: In a [-3rb], the greatest lower bound of two elements $x$ and $y$ is the "largest" element which is "less than" both $x$ and $y$, in whatever ordering the poset has.]\n\nIn a [-3rb], the greatest lower bound of two elements $x$ and $y$ is the "largest" element which is "less than" both $x$ and $y$, in whatever ordering the poset has.\nIn a rare moment of clarity in mathematical naming, the name "greatest lower bound" is a perfect description of the concept: a "lower bound" of two elements $x$ and $y$ is an object which is smaller than both $x$ and $y$ (it "bounds them from below"), and the "greatest lower bound" is the greatest of all the lower bounds.\n\nFormally, if $P$ is a [3jz set] with partial order $\\leq$, and given elements $x$ and $y$ of $P$, we say an element $z \\in P$ is a **lower bound** of $x$ and $y$ if $z \\leq x$ and $z \\leq y$.\nWe say an element $z \\in P$ is the **greatest lower bound** of $x$ and $y$ if:\n\n- $z$ is a lower bound of $x$ and $y$, and\n- for every lower bound $w$ of $x$ and $y$, we have $w \\leq z$.\n\n[todo: examples in different posets]\n[todo: example where there is no greatest lower bound because there is no lower bound]\n[todo: example where there is no GLB because while there are lower bounds, none of them is greatest]',
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