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Originally Posted by stereologist
...It is provable that there is no finite decimal expansion for pi or sqrt(2).
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This is quite true.
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So no algorithm can be written that computes these values....
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This is not quite true.
What you seem to be saying is that IF you cannot compute ALL the decimal expansion (which would be impossible), then any calculation at all is worthless; it's not the "true" value.
But scientists, engineers, programmers and others who live in the "Matheverse" don't do things that way. ALL values that are
irrational (they cannot be expressed as a/b, where a and b are integers) are always expressed and used and discussed within a certain "error factor", which can be as close to zero as your heart desires. Typically, this error factor goes unspoken and assumed.
So, how accurate a value of pi do you want? If you're willing to wait long enough, the algorithms can compute a value as accurate as you like.
