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A comment on Division by zero in type theory: a FAQ. Parent comment
Alternatively, defining f(0) to be infinity (a projectively extended real number) also allows f to be continuous.
Another possibility is to define f(0) to be some kind of "bottom" value. See the following tweets by Andrej Bauer: https://twitter.com/andrejbauer/status/1268860981943439361
Continuity is important because without it we lose computability. Every computable function is continuous (in an appropriate sense).
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Alternatively, defining f(0) to be infinity (a projectively extended real number) also allows f to be continuous.
Another possibility is to define f(0) to be some kind of "bottom" value. See the following tweets by Andrej Bauer: https://twitter.com/andrejbauer/status/1268860981943439361
Continuity is important because without it we lose computability. Every computable function is continuous (in an appropriate sense).