1. SS2PL is a proper subset of the intersection of 2PL and strictness. 2. Unlike finite sets, some infinite sets are equinumerous to proper subsets of themselves. 3. In particular, 2-perfect numbers are a proper subset of \ mathcal { S }. 4. It looks like just an arbitrary proper subset of piperazines. 5. Unambiguous CFLs are a proper subset of all CFLs : there are inherently ambiguous CFLs. 6. The notion of an invariant proper subset ? is important; the so-called "'Picard group "' 7. Indexed languages are a proper subset of context-sensitive languages. 8. A "'maximal antichain "'is an antichain that is not a proper subset of any other antichain. 9. If is not reflexive, the unit ball of is a proper subset of the unit ball of. 10. Generally speaking, no proper subset of the space of distributions contains all continuous functions and is closed under differentiation.