“complement”的概念、定义、翻译、参考文献-科学参考

complement

Mathematics

Let H be a subgroup of a group G. A complement K of H is a subgroup such that

$G = H K = {h k : h \in H, k \in K}$

and $H \cap K = {e}$ . If such a complement exists, then every element can be uniquely written as hk. But a complement need not exist, nor be unique if one does.
Let A be a subset of some universal set E. Then the complement of A is the set difference E\\A and may be denoted A′ or A^c or Ā when the universal set is understood or has been specified. Complementation (the operation of taking the complement) is a unary operation on the power set of E. The following properties hold:
1. (i) E′ = Ø and Ø′ = E.
2. (ii) For all A, (A′)′ = A.
3. (iii) For all A, A ∩ A′ = Ø and A ∪ A′ = E

Computer

1. of a set, S, with respect to some universal set U. The set consisting of elements that are in U but not in S; it is usually denoted by S′, ~S, or S̶. Formally,
$S^{'} = {x | (x \in U) and (x \notin S)}$
The process of taking complements is one of the basic operations that can be performed on sets.
The set difference (or relative complement) of two sets S and T is the set of elements that are in S but not in T; it is usually written as S—T. Thus
$S^{'} = U - S$
See also operations on sets.
2. See Boolean algebra.
3. of a subgraph G′, with vertices V′ and edges E′, of a graph G, with vertices V and edges E. The subgraph consisting of the vertices V and the edges in E but not in E′.
4. See radix-minus-one complement. See also complement number system, radix complement.

Biology

A group of proteins present in blood plasma and tissue fluid that aids the body’s defences following an immune response; the genes encoding it form part of the major histocompatibility complex. Following an antibody-antigen reaction, complement is activated chemically and becomes bound to the antibody-antigen complex (complement fixation). It can cause lysis of certain types of bacteria, through the formation of a membrane attack complex, or it can render the target cell more susceptible to phagocytosis—a process called opsonization. Binding of complement components to their respective complement receptors on immune cells stimulates various defence mechanisms.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3820029/ An illustrated overview of complement activation and regulation, from the US National Library of Medicine

Philosophy

The complement of a set S is the class of objects that are not members of S. In standard set theory the complement of a set cannot itself be a set: only those things not in the set but meeting some further restriction can form a set. See separation, axiom of.

单词	complement
释义	complement Mathematics Let H be a subgroup of a group G. A complement K of H is a subgroup such that $G = H K = {h k : h \in H, k \in K}$ and $H \cap K = {e}$ . If such a complement exists, then every element can be uniquely written as hk. But a complement need not exist, nor be unique if one does. Let A be a subset of some universal set E. Then the complement of A is the set difference E\\A and may be denoted A′ or A^c or Ā when the universal set is understood or has been specified. Complementation (the operation of taking the complement) is a unary operation on the power set of E. The following properties hold: (i) E′ = Ø and Ø′ = E. (ii) For all A, (A′)′ = A. (iii) For all A, A ∩ A′ = Ø and A ∪ A′ = E Computer 1. of a set, S, with respect to some universal set U. The set consisting of elements that are in U but not in S; it is usually denoted by S′, ~S, or S̶. Formally, $S^{'} = {x \| (x \in U) and (x \notin S)}$ The process of taking complements is one of the basic operations that can be performed on sets. The set difference (or relative complement) of two sets S and T is the set of elements that are in S but not in T; it is usually written as S—T. Thus $S^{'} = U - S$ See also operations on sets. 2. See Boolean algebra. 3. of a subgraph G′, with vertices V′ and edges E′, of a graph G, with vertices V and edges E. The subgraph consisting of the vertices V and the edges in E but not in E′. 4. See radix-minus-one complement. See also complement number system, radix complement. Biology A group of proteins present in blood plasma and tissue fluid that aids the body’s defences following an immune response; the genes encoding it form part of the major histocompatibility complex. Following an antibody-antigen reaction, complement is activated chemically and becomes bound to the antibody-antigen complex (complement fixation). It can cause lysis of certain types of bacteria, through the formation of a membrane attack complex, or it can render the target cell more susceptible to phagocytosis—a process called opsonization. Binding of complement components to their respective complement receptors on immune cells stimulates various defence mechanisms. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3820029/ An illustrated overview of complement activation and regulation, from the US National Library of Medicine Philosophy The complement of a set S is the class of objects that are not members of S. In standard set theory the complement of a set cannot itself be a set: only those things not in the set but meeting some further restriction can form a set. See separation, axiom of.
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