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第298行： − 编号是一个函数的枚举，它有两个参数 e 和 x，并输出输入 x 上编号中 e-th 函数的值。可接受的数字是所有其他数字都可以转换成的数字。Friedberg 编号(以其发现者命名)是所有部分递归函数的一对一编号; 它不一定是可接受的编号。后来的研究也涉及到其他类的数字，比如递归可枚举集的类。例如，Goncharov 发现了一类递归可枚举集，对于这类集合，根据递归同构，其数值恰好分为两个类。+ − −
→Numberings
===Numberings===
===Numberings===
编号
A numbering is an enumeration of functions; it has two parameters, ''e'' and ''x'' and outputs the value of the ''e''-th function in the numbering on the input ''x''. Numberings can be partial-recursive although some of its members are total recursive, that is, computable functions. [[Admissible numbering]]s are those into which all others can be translated. A [[Friedberg numbering]] (named after its discoverer) is a one-one numbering of all partial-recursive functions; it is necessarily not an admissible numbering. Later research dealt also with numberings of other classes like classes of recursively enumerable sets. Goncharov discovered for example a class of recursively enumerable sets for which the numberings fall into exactly two classes with respect to recursive isomorphisms.
A numbering is an enumeration of functions; it has two parameters, ''e'' and ''x'' and outputs the value of the ''e''-th function in the numbering on the input ''x''. Numberings can be partial-recursive although some of its members are total recursive, that is, computable functions. [[Admissible numbering]]s are those into which all others can be translated. A [[Friedberg numbering]] (named after its discoverer) is a one-one numbering of all partial-recursive functions; it is necessarily not an admissible numbering. Later research dealt also with numberings of other classes like classes of recursively enumerable sets. Goncharov discovered for example a class of recursively enumerable sets for which the numberings fall into exactly two classes with respect to recursive isomorphisms.
A numbering is an enumeration of functions; it has two parameters, e and x and outputs the value of the e-th function in the numbering on the input x. Numberings can be partial-recursive although some of its members are total recursive, that is, computable functions. Admissible numberings are those into which all others can be translated. A Friedberg numbering (named after its discoverer) is a one-one numbering of all partial-recursive functions; it is necessarily not an admissible numbering. Later research dealt also with numberings of other classes like classes of recursively enumerable sets. Goncharov discovered for example a class of recursively enumerable sets for which the numberings fall into exactly two classes with respect to recursive isomorphisms.
A numbering is an enumeration of functions; it has two parameters, e and x and outputs the value of the e-th function in the numbering on the input x. Numberings can be partial-recursive although some of its members are total recursive, that is, computable functions. Admissible numberings are those into which all others can be translated. A Friedberg numbering (named after its discoverer) is a one-one numbering of all partial-recursive functions; it is necessarily not an admissible numbering. Later research dealt also with numberings of other classes like classes of recursively enumerable sets. Goncharov discovered for example a class of recursively enumerable sets for which the numberings fall into exactly two classes with respect to recursive isomorphisms.
编号是函数的枚举；它有两个参数，e和x，并在输入x的编号中输出第e函数的值。编号可以是部分递归的，尽管它的一些成员是完全递归的，即可计算的函数。'''<font color="#ff8000">容许编号 Admissible numbering</font>'''是所有其他编号都可以翻译成的编号。'''<font color="#ff8000">弗里德伯格编号 Friedberg numbering</font>'''(以其发现者命名)是所有部分递归函数的一对一编号; 它不一定是容许编号。后来的研究也涉及到其他类的编号，比如递归可枚举集的类。例如，贡恰罗夫发现了一类递归可枚举集，对于这类集合，根据递归同构，其编号恰好分为两个类。
===The priority method===
===The priority method===