11. As such, a minimizer may not exist, even though an infimum would exist. 12. Complete lattices are partially ordered sets, where every subset has an infimum and a supremum. 13. In this case, the infimum is set intersection, and the supremum is set union. 14. Similarly, the infimum of such a set is called the limit inferior, or liminf. 15. Modern solution concepts not only consists of minimality notions but also take into account infimum attainment. 16. Zero is the supremum of the empty set and the infimum of " P ". 17. Where the infimum is taken over all f in L ^ + with f \ ge \ phi. 18. We notice that the infimum is taken over compact sets and hence can be replaced by a minimum. 19. What is uniquely determined by a module is the infimum of the numbers of the generators of the module. 20. This order has the desirable property that every subset has a supremum and an infimum : it is a complete lattice.
