Re: Demonstrating that 0.999... = 1

From: Michael Lockhart (ml1000_at_bellsouth.net)
Date: 09/16/04 

Date: Thu, 16 Sep 2004 18:59:36 -0400

"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
news:e92kk0ttgjcompkkcpnntrgo669v7icug9@4ax.com...
> On Thu, 16 Sep 2004 15:37:48 GMT, prl@cyclops.com (PRL) wrote:
> (*) 0.999... is the number x with this property: you can make
> the finite decimal .999...9 as close to x as you want, just
> by taking enough digits.
>
> You might want to note that first that _is_ the definition,
> whether you like it or not, and second that whether you
> like it or not you _should_ like it, because once you've
> convinced someone that that _is_ the definition it seems
> quite likely that you will also have succeeded in your
> quest to convince him that 0.999... = 1, in a manner which
> is a lot simpler than your OP. Because he's going to _agree_
> that you can make 0.999...9 as close to 1 as you want,
> just by taking enough digits!

I think that's a particularly good way of phrasing it. The next time
someone asks me about 0.999... and 1, I'll mention that and see if that sets
them straight right off.

Michael

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