Prove that the set of integers has neither a greatest nor a least element. I was given a hint: There are 2 different non existence results to prove, so prove them as separate propositions or claims. Divide into cases using the definition of the set of integers. So I was kind of confused on the hint. The way I was going to solve this was to divide into 2 cases and use induction. One case would involve using induction to prove their is no greatest element and one case would involve using induction to prove their is no least element. Am I even on the right track here? If this is not the way to go then I dont really know how to go about it.