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Re: Computing pi (or not)
Posted:
Sep 17, 2012 10:38 AM
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Dave L. Renfro wrote (in part):
http://mathforum.org/kb/message.jspa?messageID=7890876
> with an infinite number of decimals. Now it is true that there
> are algorithms that output certain numbers with an infinite
> number of decimals. For example, one such algorithm is to always
> output 3, another is to encode one of the ways of computing the
> digits of pi, and still another is to concatenate (in the appropriate
> order) the algorithms you alluded to in order to output the
> number 0.1234567891011121314...9899100101102103... Note that
> this last number has every finite decimal string appearing
> (infinitely many times, in fact), so we don't have to appeal
By the way, when I said "to concatenate", you can't always
concatenate algorithms to get an algorithm. However, in this
case each of the algorithms has a "finite run time", so I think
we're O-K by doing this here.
Dave L. Renfro
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