A Friendly Chat About Whether 0.999… = 1

Via reddit I stumbled upon this site which talks about something called hyperreal numbers and claims that in this theory, the equation 0.999… = 1 is false.

For those who follow the internet, the question of whether 0.999…=1 has come up a quadbrazillion times on practically every math related forum and even the non-math ones. And every single time it turns into this huge argument with

non-mathematicans vs frustrated-mathematicians

and neither of them winning. Some mathie forums even have strict rules banning users against posting topics that deal with 0.999….=1.

But the site mentioned above actually gives some decent points to support why 0.999…=1 isn’t necessarily true., but you have to change some of the concepts that we take for granted.

In my opinion, 0.999… and 1 are as equal as can be.

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2 Comments.

  1. It’s certainly false in the hyperreals, but results in the hyperreals cannot be extended (in general) to results on the reals. Indeed, 0.999… still equals 1 in the standard analysis of the reals.

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  2. 1/3=0.(3) 3*1/3=3/3=1 3*0.(3)=0.(9) 0.(9)=1

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