Assertion: real number | /r/HasProperty | computable
Facets:
Source sentences:
text: A real number may be either computable or uncomputable; either algorithmically random or not; and either arithmetically random or not.
text: Some constructivists accept the existence of only those reals that are computable.
text: A real number is called computable if there exists an algorithm that yields its digits.
text: Therefore, almost all real numbers are non-computable.
text: A real number a is computable if it can be approximated by some computable function f :
text: A real number is computable if and only if there is a computable Dedekind cut D corresponding to it.
text: The arithmetical operations on computable numbers are themselves computable in the sense that whenever real numbers a and b are computable then the following real numbers are also computable: a + b, a - b, ab, and a/b if b is nonzero.
text: A real number is computable if and only if the set of natural numbers it represents (when written in binary and viewed as a characteristic function) is computable.
text: A real number is computable if its digit sequence can be produced by some algorithm or Turing machine.