On Jun 26, 3:40 pm, Virgil <Vir...@home.esc> wrote: > In article > <1a5a0da4-01d1-41c5-b64b-dcc53e5ce...@k39g2000yqb.googlegroups.com>, > > > > > > Charlie-Boo <shymath...@gmail.com> wrote: > > On Jun 25, 3:25 pm, Virgil <Vir...@home.esc> wrote: > > > In article > > > <adaa005c-c180-4ce0-8d2c-81da912c6...@w12g2000yqj.googlegroups.com>, > > > > Charlie-Boo <shymath...@gmail.com> wrote: > > > > On Jun 24, 8:49 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > > > > > Charlie-Boo <shymath...@gmail.com> writes: > > > > > > On Jun 15, 2:15 am, "Peter Webb" > > > > > > >> No. You cannot form a list of all computable Reals. > > > > > > > Of course you can - it's just the list of Turing Machines. > > > > > > No, it's not. > > > > > I asked for a counterexample, to no avail. Don't you think you should > > > > substantiate your statement or retract it? > > > > > Each Turing Machine represents some computable real (all computable > > > > reals are included) and you can list those Turing Machines. The > > > > Turing Machine represents it as well as any other system of > > > > representation. > > > > Aren't there Turing machines that don't represent any real at all? > > > No. In general terms, every TM computes some result from its input. > > Agree? Then if we start with an empty tape, it represents a > > constant. How we map its execution history determines which real > > number that represents. There is generally a way to indicate which > > actions constitute output, which is needed when we use an infinite > > representation such as its real number binary expansion. > > > If the executon history can be finite, we can map all finite strings > > into real numbers, as well as the infinite ones as described above. >
> How does one associate TMs which are nonterminating but cyclic and whose > cycle depends on the input tape?- Hide quoted text -
It's a function with a rational value e.g. it calculates 1/x and when x=3 the cycles is (3). But that has nothing to do with (doesn't exist in) a system for representing constants.