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## 2007/04/16

### S-B T

D.E. Knuth，〈Computer Science and its Relation to Mathematics〉，《Selected Papers on Computer Science》p.7：

Certainly there are diverse phenomena about computers that are now being actively studied by computer scientists, phenomena that are hardly mathematical.（JK 注：如何定義 "mathematical"？）But if we restrict our attention to the study of algorithms, isn't this merely a branch of mathematics? After all, algorithms were studied primarily by matematicians, if by anyone, before the days of computing machines. Therefore one could argue that this central aspect of computer science is really part of mathematics.

However, I believe that a similar argument can be made for the proposition that mathematics is a part of computer science! Thus by the definition of set equality,the subjects would be proved equal; or at least, by the Shröder-Bernstein theorem, they would be equipotent. My own feeling is that neither of these set inclusions is valid. ...

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