 Adolf Lindenbaum showed that Ł\(_n\) is contained in Ł\(_m\) \((n \lt m)\) if and only if \(n - 1\) is a divisor of \(m - 1\), so if neither divides the other their respective tautologies properly overlap but neither set is contained in the other. Tautologies of the infinite-valued system Ł\(_{\aleph_0}\) are contained in those of all the finite-valued systems.