I am looking for an example of each:
1) A non-trivial order on a set A such that there are infinitely many minimal elements
2) A non-trivial order on a set A such that there are infinitely many maximal elements.
I was thinking that A could bet the set of ℝ. For a,b∈A, a≤b iff a+b. I don't know if this is trivial or not because it is true for both; there are infinitely many minimals or maximals. But I need two different examples.
"Order" meaning a relation that is reflexive, transitive, and anti-symmetric.
All examples are welcome, mathematical or not. Thank you!