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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 ...
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.
is a (topological) complement or supplement to if it avoids that pathology — that is, if, topologically, =. (Then M {\displaystyle M} is likewise complementary to N {\displaystyle N} .) [ 1 ] Condition 2(d) above implies that any topological complement of M {\displaystyle M} is isomorphic, as a topological vector space, to the quotient vector ...
The support of is the smallest subset of with the property that is zero on the subset's complement. If f ( x ) = 0 {\displaystyle f(x)=0} for all but a finite number of points x ∈ X , {\displaystyle x\in X,} then f {\displaystyle f} is said to have finite support .
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 .
Informally, it is called the perp, short for perpendicular complement. It is a subspace of . Example. Let = (, , ) be the vector ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
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 ...