Let R ba a partial order on S, and suppose that x is a unique minimal element in S.
a) prove that S is finite, then xRy for all s in S
b) show that the conclusion in (a) need not be true if S is infinite
(a) For any y in S, since R is a partial order on S, then if y is not a minimal element in S, we can find y1 in S, such that
y1Ry; if y1 is not a minimal element in S, we can find y2 in S, such that y2Ry1; and so on. Since S is ...
This is a discrete structures proof regarding a partial order.