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Re: adding irrational numbers
Posted:
Aug 12, 2012 9:37 AM
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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
> > >addition.
> >
> > ???????? 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
> > "procedure of addition".
>
> 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
Adorning every public street
And seem to breathe in stone, or
Move their marble feet.
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