In article <hbAg2.34$OU.66@nnrp2.clara.net>, "Bob Street" <bob@belgrave.clara.net> wrote: > > ullrich@math.okstate.edu wrote in message > <75u69b$5c3$1@nnrp1.dejanews.com>... > >In article <36825BBA.F0B079DF@ashland.baysat.net>, > > Mike Deeth <mad@ashland.baysat.net> wrote: > > [snip] > > >> > >was no such thing as an 11-year-old crackpot, because an 11-year-old > >could not possibly have developed the requisite arrogance. I've > >never seen an 11-year-old before who was convinced he was right about > >something when _all_ the mathemticians in the world said he was > >wrong. > > When I was 11, I knew _everything_. > > Now, through the mists of time and experience, I've gained some _wisdom_. I > know that there are a lot of people who know a lot more than me about a lot > of things. > > I don't _like_ it, but I accept it. > > NeoNate: At the risk of boosting your ego too much,
Don't worry about that. Especially since...
> I've enjoyed this. In > particular, Cantor's Diagonal has gone from being something that occupied a > few minutes of an Analysis lecture to being a close personal friend. And > your use of binary has been useful
Especially since you seem confused about who you're talking to - the bit you quote above is something I wrote, but there's no "use of binary" due to me anywhere here. (Maybe it was Ulrich? We clarified that Ulrich <> Ullrich earlier, right?)
In any case, ego has nothing to do with the countablility of the power set of the integers.
> - a really really strict statement of > Cantors Diagonal (for a general 'digit' set of cardinality >1, and avoiding > number/representation issues) for the real numbers is easier in bases 3 and > over than it is in binary - in any other base, one can pick _two_ digits > other than 'nine' (the largest digit), and easily prove that a diagonal can > be constructed which doesn't end in a seq of 'nines'. This is tougher in > binary.
Indeed, the fact that the proof is a little trickier in binary was "discovered" here on sci.math some time ago. (Alas the discoverer took it as the reals were countable in binary...)
David C. "that's Ullrich, not Ulrich" Ullrich
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