"Tim Little" <tim@little-possums.net> wrote in message news:slrni1obal.jrj.tim@soprano.little-possums.net... > On 2010-06-19, Marshall <marshall.spight@gmail.com> wrote: >> On Jun 18, 6:09 pm, Tim Little <t...@little-possums.net> wrote: >>> On 2010-06-18, Peter Webb <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: >>> >>> > The number that is produced is clearly "computable", because we have >>> > computed it. >>> >>> I see you still haven't consulted a definition of "computable number". >>> No worries, let me know when you have. >> >> I suggest it would be more persuasive if you made whatever >> point you have in mind about the definition of computable number >> directly. Simply repeating this one-liner makes it seem like >> you might not have a point. > > True. I was simply losing patience. I had in fact provided the > relevant point three times already, but the point was ignored each > time. > > One suitable definition: a computable real x is one for which there > exists a Turing machine that given a natural number n, will output the > n'th symbol in the decimal representation of x. (There are other > equivalent definitions, but this one seems most relevant to the > current discussion) >
Fine by me.
> The relevant point: the *only* input to the Turing machine in the > definition is n. The rest of the tape must is blank. Peter > apparently believes that a number is still computable even if the > Turing machine must be supplied with an infinite amount of input (the > list of reals). >
No.
> > - Tim
You seem to agree that the computable Reals are countable.
Do you agree that Cantor's diagonal proof when applied to a purported list of all computable Reals will produce a computable Real not on the list, thus proving that no list of all computable Reals can be formed?
