How could I start proving this:
Let $n \geq 2$. Does the set $\mathbb{Z^n}$ under dictionary order satisfy the greatest lower bound property? If so, prove it. If not, provide (and prove) a counterexample.
How could I start proving this:
Let $n \geq 2$. Does the set $\mathbb{Z^n}$ under dictionary order satisfy the greatest lower bound property? If so, prove it. If not, provide (and prove) a counterexample.