123.3 + 0.1 is 123.3999999999 ?

[Moshe Zadka]

On Thu, 5 Jun 2003, "Andrew Dalke" <adalke at mindspring.com> wrote:

> This is in agreement with the statement you and Moshe mentioned.
> Reals are reals, and only reals.  There are models related to reals
> but which are not reals, and so while it may be that in some models
> 0.99999..... != 1, that isn't the case for R.

Again, I reiterate that if you move to non-standard analysis, you want
to be careful about what you mean with 0.999...
The usual definition is lim (1-0.1**n) as n tends to infinity. But
which n would we be talking about? If you're talking about standard
natural numbers, then a limit does not exist (the property of increasing
sequences to have a limit is second order). If you're talking about
non-standard natural numbers, it's 1 (but the notation 0.9999...
is misleading).
-- 
Moshe Zadka -- http://moshez.org/
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Riley: Yeah, a lot of young people nowadays are experimenting with shortness.
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