#1, RE: Erroneous proof (???): The real interval <0,1> as a countable set.
Posted by alexb on Dec-04-00 at 06:02 PM
In response to message #0
>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?
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