Is the order relation in this problem well-defined?

Question

A friend and I are working through Munkres' topology text, and are having trouble on the problem shown. It seems to me that without defining a method to obtain n the order relation makes no sense. Am I missing something?

Answer 1

There's just a missing quantifier:

$\bf x < \bf y$ if there exists $n \in \omega$ such that $x_n < y_n$ and $x_i = y_i$ for $i > n$.