ON NON-COMPUTABLE FUNCTIONS
ON NON-COMPUTABLE FUNCTIONS
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DOI：
10.1002/j.1538-7305.1962.tb00480.x
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发表时间：
1962-01-01
影响因子：
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通讯作者：
RADO, T
中科院分区：
文献类型：
--
作者：
RADO, T
本文中使用的不可计算函数的构造是基于非负整数的有限非空集具有最大元素的原理。此外，该原则仅用于当前标准定义非常明确的集合。没有使用可计算函数的枚举，在这个意义上，没有采用对角过程。因此，一个在数学的各个领域中经常使用的明显的不证自明的原则，似乎产生了非构造性的实体。
The construction of non‐computable functions used in this paper is based on the principle that a finite, non‐empty set of non‐negative integers has a largest element. Also, this principle is used only for sets which are exceptionally well‐defined by current standards. No enumeration of computable functions is used, and in this sense the diagonal process is not employed. Thus, it appears that an apparently self‐evident principle, of constant use in every area of mathematics, yields non‐constructive entities.