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bounded lattice
A lattice $L$ is said to be bounded from below if there is an element $0\in L$ such that $0\leq x$ for all $x\in L$. Dually, $L$ is bounded from above if there exists an element $1\in L$ such that $x\leq 1$ for all $x\in L$. A bounded lattice is one that is bounded both from above and below.
For example, any finite lattice $L$ is bounded, as $\bigvee L$ and $\bigwedge L$, being join and meet of finitely many elements, exist. $\bigvee L=1$ and $\bigwedge L=0$.
Remarks. Let $L$ be a bounded lattice with $0$ and $1$ as described above.

$0\land x=0$ and $0\lor x=x$ for all $x\in L$.

$1\land x=x$ and $1\lor x=1$ for all $x\in L$.

As a result, $0$ and $1$, if they exist, are necessarily unique. For if there is another such a pair $0^{{\prime}}$ and $1^{{\prime}}$, then $0=0\land 0^{{\prime}}=0^{{\prime}}\land 0=0^{{\prime}}$. Similarly $1=1^{{\prime}}$.

$L$ is a lattice interval and can be written as $[0,1]$.
Remark. More generally, a poset $P$ is said to be bounded if it has both a greatest element $1$ and a least element $0$.
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