
Why is 0.99999 equal to 1? - ColinWright
This is an old standby, recurring (if you&#x27;ll excuse the pun) on a regular basis in many, many forums.  It never seems to be settled to everyone&#x27;s satisfaction, so I&#x27;d bet there are people here on HN who don&#x27;t believe that 0.999999... is equal to 1.<p>I would be interested in engaging with a few, in part to help them see why modern mainstream mathematics says that, in part to try to help me understand their point of view, and in part to test an idea I have about a discussion system.<p>I&#x27;m intending this to take part over a few weeks, and I won&#x27;t always be able to respond instantly to questions, so it would favour anyone interested in a thoughtful discussion.  If you&#x27;re interested, please feel free to send me an email - details are in my profile.<p>Thanks.
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dozzie
As usual, somebody undereducated mistakes notation ("0.9999...") for the real
thing (a number).

Real numbers (and even rational numbers) are dense: pick any two that are
different and you'll find a third one different than the two that is between
them. You can't do that with 1 and this "0.9999..." thing.

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CarolineW
Forgive me, but you have me slightly confused. You say:

 _> As usual, somebody undereducated mistakes notation ("0.9999...") for the
real thing (a number)._

To whom are you referring?

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geophile

      1/3 = 0.3333...
      Multiply each side by 3
      3 * (1/3) = 1
      3 * 0.3333... = 0.9999...
    

So 1 = 0.9999...

