Of course the problem with that analysis is that there is no "last
digit" in the series which you can fix at 1 or 8 or 7, etc.

One that I am still not really able to get my head around is that the
order of the elements in an infinite series matters if the elements
alternate in sign.

For example, the sum of 1/x from x=3D1 to x=3Dinf does not converge.

Also, the sum of 1/x from x=3D1 to x=3Dinf where x is odd (or even) also
does not converge.

BUT, the sum ((-1)^x)/x from x=3D1 to x=3Dinf does converge (call this C)

AND (drum roll please), B minus A does NOT converge, where A=3Dsum of
1/x from x=3D1 to x=3Dinf where x is odd and B is the same where x is
even.

YET, you can interleave the terms of A and B and get a series which
DOES converge (given as C above).

This means that, once you get to an infinite number of terms in a
series, addition is no longer commutative or associative.

Sean


On Fri, Jul 17, 2009 at 11:53 PM, Russell McMahon<apptechnz@gmail.com> wrot=
e:
>> 1.999999... =3D=3D 2.000000...
> And 1.9999... =3D 1.9999...8 + 0.000 ...1
> And 1.999...8 =3D 1.999...7 + 0.000 ...1
> And ...
>
> And 2.000...1 =3D ...
>
> After a while you spiral into the sun, or get flung off into outer space,
> while still arguing about the logical fallacies (and falacial logics) of
> infinite series et al.
>
> :-)
>
> Flame shields up ...
>
> =A0 =A0 R
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