a set $A = \{1,2,4,8,16\}$, the relation is divide '$|$'. How do i prove that it is Total Order Relation for this set.
i know that for a set to be total order relation, it has to be partial order relation and all elements in the sets are comparable.
i can prove that the set is reflexive, anti-symmetric and transitive but however how do prove that this set is comparable. Thank You!
Rewrite $A=\{2^i|i \in \{ 0,1,2,3,4\} \}$
Given two element, $2^i,2^j \in A$, prove that $2^i | 2^j$ if and only if $i \leq j$.
Note taht $2^i | 2^j$ means $2^i R 2^j$.