Re: rational or irrational?

Your Subject field is spelled correctly, but your article has some
apparent typos:

> From: "Nurxgwkk" <wildlife@xxxxxxxxxxx>
> is 0.00000000.....0000001 with and infinite amount of zeros in-between
^
(Do you mean "an" instead of "and"?)

> an irrantional number or not?
^
(Do you mean "irrational" instead of "irrantional"?)

Assuming those typos fixed as I suggested, there are two issues
involved here: The string of digits you are trying to express, and any
number if any which is thereby expressed.

Let's tackle an easier and well-defined example first:
0.1000000000... (with an infinite amount of trailing zeroes)
That notation has a clear meaning. There is an infinitely long array of
digits, indexed by 0, -1, -2, -3, ... (I'm using negative indexes so
the power of ten matches the index rather than the negative of the
index, reserving positive indexes for any digits to the left of the
units position, which doesn't apply here, but would apply with other
examples using the same notational system.)
digit[0] = '0'
digit[-1] = '1'
digit[-n] = '0' for all other values of n (2,3,4,...)

The set of digits is of ordinality -omega, i.e. like omega but running
the opposite direction (from 0 downward into negative integers instead
of upward into positive integers).

But in your case, it's not clear what your set of indexes for the
digits are supposed to be? How do you put an infinite number of indexes
*between* two fixed endpoints, while still having the digits near
either fixed endpoint be descrete like a sequence or reverse sequence?
Like it's easy to get this part:
0.0000
with indexes 0, -1, -2, -3, and -4,
and this part:
0001
with indexes N+3, N+2, N+1 and N, for some abstract symbol N,
but how do you get an infinite number of digits between them?
..............
What set of indexes for those digits are you presuming?

After you answer that question, *then* we might be able to find any
meaning to those digits representing any number.
.

Relevant Pages

  • Re: The Modified Halting Problem, Take ??? .
    ... What you write is not the same as saying all digits can be computed. ... With an infinite number the same process is used, ... We have infinitely many halting TMs, ... first you see 3 on the first tape, then you see 3.1 on the second tape, ...
    (sci.logic)
  • Re: The Modified Halting Problem, Take ??? .
    ... What you write is not the same as saying all digits can be computed. ... With an infinite number the same process is used, ... first you see 3 on the first tape, then you see 3.1 on the second tape, ... There are countably infinite Turing machines (meaning exactly TMs ...
    (sci.logic)
  • Re: abundance of irrationals!)
    ... >> aeo6 Tony Orlow wrote: ... >>> You claim an infinite set ... >> unlimited number of nonzero digits, do you think that if you ...
    (sci.math)
  • Re: infinity
    ... If p can take on infinite values, ... There is no reason to restrict your digits to finite positions. ... Every '9' digit corresponds to a member in set S ... finite strings ona finite alphabet, since the number of strings is finite for ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> ending with an reversed infinite sequence of zeros, ... >> must ask where the intitial digits and terminal digits get connected to ... how do the initial or terminal digits connect up with them. ...
    (sci.math)