Dr. Dobb's Python-URL! - weekly Python news and links (Mar 17)
Erik Max Francis
max at alcyone.com
Wed Mar 19 22:25:04 CET 2003
"Chermside, Michael" wrote:
>  A really interesting argument can be made that it's got just as
> many 9's as 0's, since "x.00000..." = "(x-1).99999..." by most
> definitions. Does this mean that integers are normal in base 2?
No, because either it's got an infinite number of zeroes or an infinite
number of ones. Neither expansion is normal (they contain exactly none
of the other digit), and you can't include both simultaneously.
Furthermore, normality or non-normality can only be properties of normal
numbers, and both of these expansions terminate or repeat, meaning that
they are rational, not irrational. So therefore the normal/non-normal
qualification can't apply at all.
Erik Max Francis / max at alcyone.com / http://www.alcyone.com/max/
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