Explore a comprehensive lecture on Vergleichsstellensätze for ordered semirings, presented by Tobias Fritz at the Centre de recherches mathématiques (CRM) Workshop on Tensors. Delve into the semiring structure of tensors and resource theories in quantum information, examining two theorems that strengthen Strassen's separation theorem by weakening its Archimedeanicity assumption. Learn about the criteria for asymptotic and catalytic resource convertibility, and discover applications in random walks, representation theory of SU(n), and matrix majorization. Gain insights into how these Vergleichsstellensätze make asymptotic and catalytic orderings computable, providing simple formulas for asymptotic conversion rates. Follow the lecture's progression through motivation, theorem assembly, neutral elements, Strassen's version, non-examples, preorder generalization, and catalytic artery, concluding with a summary of key concepts.