Dividing by Zero - How Bad Is It, Really?

  title={Dividing by Zero - How Bad Is It, Really?},
  author={Takayuki Kihara and Arno Pauly},
In computable analysis testing a real number for being zero is a fundamental example of a non-computable task. This causes problems for division: We cannot ensure that the number we want to divide by is not zero. In many cases, any real number would be an acceptable outcome if the divisor is zero - but even this cannot be done in a computable way. In this note we investigate the strength of the computational problem "Robust division": Given a pair of real numbers, the first not greater than… 

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