Infimum (source code)
= Infimum
{title2=$\inf$}
= Infima
{synonym}
For a nonempty <set> $A\subseteq\mathbb R$, a real number $\ell$ is its <infimum> precisely when it is a <lower bound> and every other <lower bound> is at most $\ell$. It is the <greatest lower bound>, not necessarily the <minimum>.
For $C=\{1/n:n\in\mathbb N_{>0}\}$, zero is a <lower bound>. Every positive candidate $\varepsilon$ fails: the <Archimedean property> gives an <integer> $n>1/\varepsilon$, hence $1/n<\varepsilon$. Thus $\inf C=0$, although zero is never a member of $C$. This is the lower-edge counterpart of approximating an unattained <supremum>.
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