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Replies: 14   Last Post: Oct 10, 2012 3:13 PM

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 Frederick Williams Posts: 2,166 Registered: 10/4/10
Posted: Aug 12, 2012 9:37 AM

calvin wrote:
>
> On Aug 11, 12:57 pm, David C. Ullrich <ullr...@math.okstate.edu>
> wrote:

> > On Fri, 10 Aug 2012 20:25:12 -0700 (PDT), calvin wrote:
> > >Let i1 = .010010001000010000010000001...
> > >and i2 = .101101110111101111101111110...

> >
> > >Clearly both of these non-repeating decimals
> > >are irrational, and their

> >
> > >sum i3 = .111111111111111111111111111...
> > >which is repeating, rational, and = 1/9

> >
> > >One could easily make up numerous examples
> > >similar to this one of pairs of irrationals whose
> > >sum is rational, and others whose sum is
> > >irrational.

> >
> > >Note that in the above case the sum is arrived
> > >at by simple intuition, not by any procedure of

> >
> > ???????? It's not at all clear what that means.
> > In any case, if you're given two numbers, rational
> > or not, expressed as infinite decimals, then the
> > decimal expansion of the sum _is_ given by a

>
> I just intuitively overlaid i1 on top of i2.

My thought: "procedure of addition" equals terminating algorithm; and
there is none such for infinite decimals. Despite that, in particular
cases one may find the answer, so that is by "simple intuition".

--
The animated figures stand
And seem to breathe in stone, or
Move their marble feet.

Date Subject Author
8/10/12 Calvin
8/11/12 quasi
8/11/12 Richard Tobin
8/11/12 Calvin
8/11/12 Calvin
8/11/12 quasi
8/11/12 quasi
10/9/12 Calvin
8/11/12 David C. Ullrich
8/12/12 hagman
8/11/12 David C. Ullrich
8/11/12 Calvin
8/12/12 Frederick Williams
10/10/12 dan73