Consider a [partial ordering,](Partial%20ordering.md) $(A,<),$ and a non-[empty](Subsets.md#Empty%20subsets) [subset,](Subsets.md) $B$ of $A.$ If $a\in A,$ then $a$ is the _least element_ of $B$ if $a\in B$ and for all $b \in B$, $a\leq b.$^0f003b %%From page 17 of Jech%% #MathematicalFoundations/SetTheory