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In Leegin Creative Leather Prods., Inc. v. PSKS, Inc., 127 S. Ct. 2705 (2007), the Supreme Court considered whether federal antitrust law established a per se ban on minimum resale price agreements and, instead, allow resale price maintenance agreements to be judged by the rule of reason, the usual standard applied to determine if there is a ...
A subset of is called meagre in, a meagre subset of , or of the first category in if it is a countable union of nowhere dense subsets of . [1] Otherwise, the subset is called nonmeagre in X , {\displaystyle X,} a nonmeagre subset of X , {\displaystyle X,} or of the second category in X . {\displaystyle X.} [ 1 ] The qualifier "in X ...
The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible.The axiom is usually written as V = L.The axiom, first investigated by Kurt Gödel, is inconsistent with the proposition that zero sharp exists and stronger large cardinal axioms (see list of large cardinal properties).
Then the negligible sets form an ideal. This idea can be applied to any infinite set; but if applied to a finite set, every subset will be negligible, which is not a very useful notion. Or let X be an uncountable set, and let a subset of X be negligible if it is countable. Then the negligible sets form a sigma-ideal.
The red subset = {1,2,3,4} has two maximal elements, viz. 3 and 4, and one minimal element, viz. 1, which is also its least element. In mathematics , especially in order theory , a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any other element in S ...
More precisely, every element s of the minimal model can be named; in other words there is a first-order sentence φ(x) such that s is the unique element of the minimal model for which φ(s) is true. Cohen (1963) gave another construction of the minimal model as the strongly constructible sets, using a modified form of Gödel's constructible ...
Note that a (usual) set cover is equivalent to a fractional set cover in which all fractions are either 0 or 1; therefore, the size of the smallest fractional cover is at most the size of the smallest cover, but may be smaller. For example, consider the universe U = {1, 2, 3} and the collection of sets S = { {1, 2}, {2, 3}, {3, 1} }.
In this example, C = {S 1, S 4} is a set cover; this corresponds to the dominating set D = {1, 4}. D = {a, 3, 4} is another dominating set for the graph G. Given D, we can construct a dominating set X = {1, 3, 4} which is not larger than D and which is a subset of I. The dominating set X corresponds to the set cover C = {S 1, S 3, S 4}.