Practice question · Multiple choice
Calculus assumes exact real numbers and computers have neither exact reals nor infinitely many of them. Why is numerical computing nevertheless trustworthy?
Hints
- Ask what a numerical analyst computes alongside the answer.
- The goal is not exactness. What is it?
Show the answer
A. Because methods come with error analysis, so you get a bound
Why
The discipline is bounding the error rather than pretending it away: truncation from stopping an infinite process, round-off from the arithmetic, both quantified. Option 2 is comforting and false, errors compound in some algorithms and cancel in others, which is exactly what stability analysis is for.
Practise Limits and Continuity
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