dan73
Posts:
412
From:
ct
Registered:
6/14/08
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Re: adding irrational numbers
Posted:
Oct 10, 2012 3:13 PM
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> 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.
>
> questions:
>
> 1) Has there been any notable work done in this area?
>
> 2) Are there any known examples of irrationals not
> made up in this way which have rational sums?
>
> 3) Is there any theory of a method of adding
> irrational numbers other than the intuitive approach
> indicated above, which obviously is severely limited
> in scope?
The 9's compliment comes to mind --
The 9's compliment of pi is irrational
and = 6.8584073464102067... + pi =
9.999999999... = 10
This will happen with any irrational.
Dan
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