On 2010-06-19, Marshall <firstname.lastname@example.org> 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)
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).