Re: 0.33333333... = 1/3

From: Jon Haugsand (jonhaug_at_ifi.uio.no)
Date: 10/29/04 

Date: 29 Oct 2004 12:44:56 +0200

* Oscar Lanzi, III
> There you have it, an implicit definition in most problems.
>
> With the real number system specified there is no difficulty. 0.9999...
> converges and equals 1.

Nitpick. The number 0.999... is a _number_ and numbers don't
converge, they just _are_. Sequences (and sums) may or may not
converge.

The number 0.999... is by definition equal to the limit of the
series SUM[i=1 to N] (9/10^i) as N goes to infinity. 

-- 
Jon Haugsand
  Dept. of Informatics, Univ. of Oslo, Norway, mailto:jonhaug@ifi.uio.no
  http://www.ifi.uio.no/~jonhaug/, Phone: +47 22 85 24 92