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Computational inadequacy of decimal notation

The introduction of decimal notation, centuries ago, was a breakthrough regarding efficient approximate computation by hand--and nowadays by electronic digital computers. A perhaps surprising fact, discovered by the constructive mathematician Brouwer in 1920, is that infinite decimal numerals are are not suitable notation for exact computation. Another discovery of Brouwer is that computable functions are continuous (but see Chapter 7 below). We sketch topological proofs these two facts.



 

Martin Escardo
2000-10-02