I came across this question in a refrence book for discrete mathematics:
For a partially ordered set M with x ∈ M being the only minimal element on that set, is x the least element as well? Show your answer for finitie and infinite set M.
After long thought about this question, I believe x is indeed the least element in case of finite set M. In case of infinite set M, x isn't the least element. I am unable to find the appropriate approach to prove this though.
Any help would be greatly appreciated!