From: Steven Jenkins <steven.jenkins@...>
Date: 2004-10-29T03:29:47+09:00
Subject: Re: Rounding error, (100.0 2000 2001 Desktop Money Projects Protege.png Protege_2.1 Q3.DIR Quicken RCS Screenshot-1.png Screenshot-2.png Screenshot-3.png Screenshot.png afs-backup afshome amixer.works b basic.edl bin bruin-woods c4isr.owl c4isr.pprj cellphones.sxc comedi comedilib config config-n6uni config.austin conv-factors.sxc debian drvinfo.txt dry.xml ds-tools emachines evolution float.sxc fnfix foomatic-db-current.tar.gz grp-backup iFog-Aqua20-1.tar.gz id_dsa.pub income jimo-core-sjenkins job-search ken-cole latex2docbook letters lfront log mbse modules n6uni-etc.tar.gz n6uni-home.tar.gz n6uni.tar.gz nasa nisotr old-ruby-tools openafs photos pickaxe2.pdf rdtmerge resume rexml.sxc ruby-bug ruby-oscon.sxi ruby-tidal ruby-tools smbmount.3.0.7 software themes tidal-3-11 tidal-3-5-patches tidal-cvsroot-archive tidal-data tidal-head tidal-poster-corrected.ppt tidal-poster.ppt tidal-web tidal-xdemo tidalsim.tar.gz uuid vim-ruby-snapshot-2003-10-12 wet.xml yepp 9.95).to_i == 994

Guillaume Marcais wrote:
> Another funny failing of the notation is that not everything that looks
> like a number actually represents a number. The following is quite
> intriging:
> 
> x = 0.99999... (infinite serie of 9s)
> 10*x = 9.99999...
> 10*x - x = 9*x = 9
> So x = 1!
> 
> IIRC, any 'word' that ends with an infinite serie of 9s does not
> represent an actual real number.

Sure it does. As you just showed, .9999... == 1.0.

Decimal notation is just convention. We take it for granted, but it's 
convention. Any infinite decimal expanson is interpreted as a power 
series. Such series always converge, and you can show (as you just did) 
that any repeating decimal expansion converges to a rational number.

It's not a trick. They really are equal. Because we say so. :-)

Steve