>>r={x: xeR, xe} has a decimal
>>representation given by:
>>r= Sum(Cn 10^-n), where n =
>>1 to infinity, and Cn
>>= {0,1,...9}.
>>
>>Construct the corresponding natural number:
>>m=Sum(Cn 10^(n-1)), where n = 1
>>to infinity,
>>and Cn = {0,1,...9}.
>
>Do you know what Pi is?
>Pi = 3.14159 ...
>
>The number has an infinite decimal
>expansion. There are ways to
>find any of its digits.
>Divide it by 10 to
>get a number in the
>interval (0, 1): 0.314159 ...
>What natural number corresponds to
>this one according to your
>construction?
>
>How big is it? May you
>bound it by some power
>of 10?

I'm inclined to say the corresponding natural number is:
m = ...951413 -- and, exactly like pi, there are ways to find any of its digits (EXCEPT the "first" one -- or "last" one in the case of pi). How big and how to bound it? Hmmm. Does it HAVE to be bounded in order to be a natural number? I suspect this is the essential idea I didn't take into account: the natural numbers are generated successively (or inductively) from zero. These numbers seem to be a "granddaddy" extension of the natural numbers -- uncountable and having the cardinality of the continuum. Interesting to contemplate. I think you've helped me understand an important distinction. Thanks for your help and for this wonderful site.