# Divisibility of sequences

**Algebra**Level 3

Let \(S_n\) be the set of all sequences of natural numbers of \(n\) terms.

Let \(\{a\},\{b\}\in S_n\) and define the divisibility rule: \[\{a\}|\{b\} \Longleftrightarrow a_i|b_i \forall i=0,1,\cdots n-1\]

Considering this divisibility rule as a relation on \(S_n\), is this relation a partial order? Is this relation a total order?