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What appears to the modern reader as the representing function's logical inversion, i.e. the representing function is 0 when the function R is "true" or satisfied", plays a useful role in Kleene's definition of the logical functions OR, AND, and IMPLY, [2]: 228 the bounded-[2]: 228 and unbounded-[2]: 279 ff mu operators and the CASE function.
A p-complement is a complement to a Sylow p-subgroup. Theorems of Frobenius and Thompson describe when a group has a normal p-complement. Philip Hall characterized finite soluble groups amongst finite groups as those with p-complements for every prime p; these p-complements are used to form what is called a Sylow system.
The choice of can matter quite strongly: every complemented vector subspace has algebraic complements that do not complement topologically. Because a linear map between two normed (or Banach ) spaces is bounded if and only if it is continuous , the definition in the categories of normed (resp. Banach ) spaces is the same as in topological ...
The complement of an edgeless graph is a complete graph and vice versa. Any induced subgraph of the complement graph of a graph G is the complement of the corresponding induced subgraph in G. An independent set in a graph is a clique in the complement graph and vice versa. This is a special case of the previous two properties, as an independent ...
If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
Here the domain of the complement is the set of all integers exceeding one. [3] There is a Turing reduction from every problem to its complement problem. [4] The complement operation is an involution, meaning it "undoes itself", or the complement of the complement is the original problem.
c is continuous function. Axiom c4. Involutions c is an involution, which means that c(c(a)) = a for each a ∈ [0,1] c is a strong negator (aka fuzzy complement). A function c satisfying axioms c1 and c3 has at least one fixpoint a * with c(a *) = a *, and if axiom c2 is fulfilled as well
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement. Consider the following subtraction problem: