Lets say we have a set $A$. Suppose that $A$ is ordered by $<$, $A$ is completely ordered.
$<$ can be defined as $<:=\{(a,b) \in A\times A : a
- Given that $<$ is transitive, it is not necesary to know all the values of $<$, so what is the minimum amount of pairs in $<$ needed to know all the values of $<$. For example: Let $A = \{a,b,c,d,e\}$. Suppose we know $a, $c
, $d , $ e. From that, we can conclude that $c , so we know all the values of $<$ . - Is there an algorithm to find that/those minimum sets?