Re: [Mid] A lesson in Algorism

> >> Anyway, let x = 0.99999... (where ... means the nines continue
> >> forever).

> Be that as it may, you also multiplied 0.99999... by a factor of 10.
>It is that final "0" in the number 10 and the product of the multiplication
>that is being deliberately ignored. When you perform some math processes, you
>can actually curtail an infinite series and make it a finite, albeit long,
>series of digits. Multiplying by any factor ending in a zero or series of
>zeros before the decimal marker will frequently allow one to create the
>illusion that something is lost or gained by a mathematical exercise.
>
> You know that this is the real truth of the matter. (Heh, durned
>kids!)

Um, I'm sorry, Your Grace, but I think you are mistaken (okay, I know
you are mistaken :) ). We are not curtailing an infinite series at all.

The 0.9999... goes on forever. Multiplying it by 10 doesn't change
that at all. Nothing was gained or lost.

Look at it another way. 1 divided by 3 is 1/3, or 0.333.... (threes
forever).

Multiply that by 3 and you get 1/3 * 3 = 1, and
0.333... * 3 = 0.999... = 1

Same thing.

- Midair
From: "Charles J. Cohen" <charles@eecs.umich.edu>
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Received on Fri Jun 11 14:26:05 1999