Computable analysis

In mathematics, computable analysis is the study of which parts of real analysis and functional analysis can be carried out in a computable manner. It is closely related to constructive analysis.

Basic results

The computable real numbers form a real closed field. The equality relation on computable real numbers is not computable, but for unequal computable real numbers the order relation is computable.

Computable real functions map computable real numbers to computable real numbers. The composition of computable real functions is again computable. Every computable real function is continuous.

See also

  • Specker sequence

References

  • Oliver Aberth (1980), Computable analysis, McGraw-Hill, 1980.
  • Marian Pour-El and Ian Richards, Computability in Analysis and Physics, Springer-Verlag, 1989.
  • Stephen G. Simpson (1999), Subsystems of second-order arithmetic.
  • Klaus Weihrauch (2000), Computable analysis, Springer, 2000.