Recursive Approximability of Real Numbers

A real number is recursively approximable if there is a computable sequence of rational numbers converging to it. If some extra condition to the convergence is added, then the limit real number might have more effectivity. In this note we summarize some recent attempts to classify the recursively approximable real numbers by the convergence rates of the corresponding computable sequences of rational numbers and arithmetical reals. Mathematics Subject Classification: 03F60, 26E40, 03D80.

• Type: Journal
• Year: 2002
• Where: MLQ
• Authors: Xizhong Zheng
• Keywords: Computable Sequences, MLQ 2002, Rational Numbers, Real Numbers