How do they handle discontinuous functions like division? Since equality is undecidable, if I gave it 1/0 it could never be sure that I was dividing by zero or that the result was within 1 of the correct answer.
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That's discussed in the article. They let the calculator fail if it can't figure out in reasonable time that a number you wish to divide by is apart from zero. Also, division is not discontinuous :-) it just has a disconnected domain, and which is not decidable.
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