In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 15 Jun., 08:15, "Peter Webb" > <webbfam...@DIESPAMDIEoptusnet.com.au> > > > No. You cannot form a list of all computable Reals. If you could do this, > > then you could use a diagonal argument to construct a computable Real not in > > the list. > > Twice no. First, a number cannot be defined by an infinite sequence of > digits, because of practical reasons. (To define means to let somebody > know what is meant.)
Perhaps not in WM's minimath, but it is quite possible and frequently enough done in regular math to be standard.
>Second the list of all real definitions cannot > have a diagonal because at least two lines have only one symbol.
There is no such thing as a "list of all real definitions" because if there were, one could create a real not in it. > > Here is a list that contains not only every computable real number but > also every possible definition of every item that can be defined. > > 0 > 1 > 00 > 01 > 10 > 11 > 000 > ...
That list does not appear to contain any reals between 0 and 1, or, if they are all in [0,1], it does not contain any reals greater than 1.