0.999... = 1 (proof inside!)


Ancient Mariner
ok, here's something I've been buzzing at people for a few years (math people laugh and run from me)

0.999... (where the 9's go on to infinity) is equal to 1.

here's how:

One divided by three equals 0.333(to infinity)
(1/3) = 0.333...

Three divided by one equals three
(3/1) = 3

Also, since fractions are multiplied numerator*numerator and denominator*denominator:
(1/3)*(3/1) = (3/3) = 1

Keep in mind that 3*3 = 9, so it follows that:
(1/3)*3 = (0.333...)*3 = (0.999...)

We've used the same equation to achieve two distinct answers (3 and 3/1 are equal, remember!). Simple Junior High math allows use to substitute and eliminate common factors, so we are left with:

0.999... = 1

If you have a way of resolving this paradox, please post!

Iron Duke
Uncle Cecil always has the answer:
[a href=\'http://www.straightdope.com/columns/030711.html\' target=\'_blank\']http://www.straightdope.com/columns/030711.html[/a]
[!--QuoteBegin-thefrush+Feb 23 2004, 11:54 PM--][div class=\'quotetop\']QUOTE(thefrush @ Feb 23 2004, 11:54 PM)[/div][div class=\'quotemain\'][!--QuoteEBegin--] Uh, my head hurts... [/quote]
Crackpot theory? oh man i can't wait! I mean how can he top .999=1! sequals never mesure up to the original! except The Empire Strikes Back, but that was part of a Trilogy! So should it count? I think it should! So the remote possibility of The Crackpot Theory surpassing .999=1 does exist yet it's miniscule...I can't wait, I can't wait! [!--emo&:rock:--][img src=\'style_emoticons/[#EMO_DIR#]/headbang.gif\' border=\'0\' style=\'vertical-align:middle\' alt=\'headbang.gif\' /][!--endemo--]
[!--QuoteBegin-Onhell+Feb 27 2004, 02:40 PM--][div class=\'quotetop\']QUOTE(Onhell @ Feb 27 2004, 02:40 PM)[/div][div class=\'quotemain\'][!--QuoteEBegin--] sequals never mesure up to the original! except The Empire Strikes Back, but that was part of a Trilogy! [/quote]
The Godfather Part II. Arguably better than the first, and that's saying a lot. Also, it's the only sequel to win Best Picture.
SMX I don't know where I'd be without you... [!--emo&:rock:--][img src=\'style_emoticons/[#EMO_DIR#]/headbang.gif\' border=\'0\' style=\'vertical-align:middle\' alt=\'headbang.gif\' /][!--endemo--]
yes...... [!--emo&:unsure:--][img src=\'style_emoticons/[#EMO_DIR#]/unsure.gif\' border=\'0\' style=\'vertical-align:middle\' alt=\'unsure.gif\' /][!--endemo--]
and where does this leave us [!--emo&;)--][img src=\'style_emoticons/[#EMO_DIR#]/wink.gif\' border=\'0\' style=\'vertical-align:middle\' alt=\'wink.gif\' /][!--endemo--]
no where. its a random bit of [!--emo&:spam:--][img src=\'style_emoticons/[#EMO_DIR#]/spam.gif\' border=\'0\' style=\'vertical-align:middle\' alt=\'spam.gif\' /][!--endemo--]