[FOM] 770 in Pi

Bill Taylor W.Taylor at math.canterbury.ac.nz
Mon Jul 16 23:26:20 EDT 2007

-> to any base, and in fact almost all real numbers are normal with respect
-> to all bases at the same time.

A little query for mathies here.

It is not known for sure whether those particular numbers mentioned (pi etc)
are normal or not, even though it is virtually certain they will be.

The only numbers *known* to be normal to base 10 are in fact rather
highly structured and patternish, like this one...

.0123456789101112131415161718192021...        ...9899100101102...   ...

...where the standard numerals are merely laid out adjacently!

And it is not even known whether this number will be normal to any other
base (other than 100, 1000 etc), though again it is almost certain.

However, my query relates to the remark above.  It is indeed easy to prove
that "almost all" (in the sense of probability) reals are normal to ALL
bases.  Yet AFAIK there are no specific examples of such a one that is
known for certain - actually proved so.

Does anyone know of an example, or even a construction method for one?

             Bill Taylor          W.Taylor at math.canterbury.ac.nz
             And God said
             Let there be numbers
             And there *were* numbers.
             Odd and even created he them,
             He said to them be fruitful and multiply
             And he commanded them to keep the laws of induction

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