1. Consider the partial order ≥ on the set Z≥0 . Argue that there is no maximal element in Z 2. Note that there is a minimal element under the partial order ≥ on Z≥0—namely 0, which is also the...

1. Consider the partial order ≥ on the set Z≥0 . Argue that there is no maximal element in Z

2. Note that there is a minimal element under the partial order ≥ on Z≥0—namely 0, which is also the minimum element. Give an example of a partial order on an infinite set that has neither a minimal nor a maximal element.