**Puzzle TF3.** Let \\((X,\leq,\otimes,I)\\) be a symmetric monoidal poset, and \\(\$\in X\\) an arbitrary element. (I'm only naming the element suggestively, no further properties should be required.) Now for given \\(x,y\in X\\), define \\(\mathcal{X}(x,y)\\) to be the smallest natural number \\(n\\) such that \\(x \leq y \otimes \$^{\otimes n}\\) if such an \\(n\\) exists, and \\(\infty\\) otherwise. Prove that this makes \\(X\\) into a **Cost**-enriched category! What is its resource-theoretic interpretation?