关于实数的可计算性

On the computability of real numbers

给出了图灵机和可计算数之间的关系和可计算数的若干性质,提出了半可计算数的概念,并在此基础上结合集合的算术层次对实数集进行了算术分层,这一思想对于从可计算性角度理解实数具有借鉴意义。

The relationships between Turing Machine and computable number are described and some properties of computable number are given, a new concept called partially computable number is proposed in this paper, based on these, the real number set is divided into arithmetic hierarchies according to the basic arithmetic hierarchy theory, this idea may be helpful to understand real numbers in the opinion of computability.