# 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?

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