11. If a set and has the same cardinality as a proper subset of itself, then it's an infinite set. 12. A system of equations if " independent " if it is not equivalent to a proper subset of itself. 13. A frame is an " exact frame " if no proper subset of the frame spans the inner product space. 14. I therefore consider " toroids " to be a proper subset of all " surfaces / solids of revolution ". 15. If I and J are stable models of the same logic program then I is not a proper subset of J. 16. Any proper subset of a finite set " S " is finite and has fewer elements than " S " itself. 17. In 1881 he set out the set that can be put into a one-to-one correspondence with one of its proper subsets . 18. A generating set of a module is said to be "'minimal "'if no proper subset of the set generates the module. 19. The first two complement laws above show that if is a non-empty, proper subset of, then } } is a partition of. 20. Actually, proper subsets of \ mathfrak X may host sentineling tasks that prove harder than those emerging with \ mathfrak X itself.
