Ordering of Reciprocals/Proof 1

Proof
By Reciprocal Function is Strictly Decreasing, the reciprocal function is strictly decreasing.

By Mapping from Totally Ordered Set is Dual Order Embedding iff Strictly Decreasing, the reciprocal function is a dual order embedding.

That is:
 * $x \le y \iff \dfrac 1 y \le \dfrac 1 x$