Exercise
81
[1YJ] Consider \(A=ℝ^ 2\) and consider the relation
\[ (x,y)⪯ (x',y') \iff ( x≤ x'∧ y≤ y') \]
show that it is an order relation; is it partial or total?
Define \(B=\{ (x,y):x^ 2+y^ 2 ≤ 1\} \), let’s consider it as an ordered set with the sorting \(⪯\) : are there maxima? minima? maximals? minimals?