
A graphic illustration of 0.999…=1 - joshuacc
http://plasmasturm.org/log/0.999/
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webfuel
Wikipedia has a great article on this: <http://en.wikipedia.org/wiki/.999>

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jsmcgd
I am a bit disappointed there weren't any graphics but a reasonable
explanation nonetheless.

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neodawn
This question was posed by my math teacher to the class during a lean time in
class for fun during my engineering days. This was my answer.

x = 0.999999....... (1)

10x = 9.999999....... (2)

Perform (2) minus (1)

9x = 9

x = 1

When I wrote it on the board, I still remember the awe in my friend's faces.
And all I was doing was using the standard method to convert a recurring
decimal into a fraction. :)

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dfxm12
"Because: it isn’t there. There is no difference. They are the same."

Was Mt. Everest still not the highest mountain even before it was discovered?
The need for "seeing is believing", applied to math is pretty childish.

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to3m
Apologies, not all of us are able to see straight through to the truth in
every case. This argument convinced me (not least because it occurred to me
too a few years ago ;) - I hadn't seen it anywhere before at the time, though
I'm sure this is because (a) I hadn't spent much time looking, and (b) to
those skilled in the art, it is so obvious as to be barely worthy of comment.

If you're simply not convinced by his line of thought (it's hard to tell...),
an alternative argument might be: noting that 3 multiplied by one third is 1,
consider what that would look like if written out in decimal notation.

(I am sure there are plenty more arguments too, probably much better than
mine.)

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dimitar
0.(999) = 1 - 1/inf this should be intuitive.

and since 1/inf is 0

0.(999) = 1

Check the same reasoning in mathematical notation:
[http://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4...](http://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png)

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tbh2347
Not to be that guy, but technically (0.999) = 1 - 10^(-inf).

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rsoto
I was expecting a graphic illustration.

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parfe
I find it funny that people have no problem understanding that 9/9 = 1 or .5 *
2 = 1 or 1/9 * 9 = 1 but suddenly when represented as 0.999... = 1 the matter
becomes debatable.

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corin_
I don't see how that's really surprising. Your examples are all easily
explainable to a very young child and can be described in physical terms, "9
apples split between 9 people", "half a cake times two" - even people who
don't need such simplistic thoughts, the fact that it is relatable to real
life does make it easier to grasp.

Whereas 0.999... just isn't relatable at all, it's a concept that purely
exists for the sake of mathematics.

Not to mention, your examples are all sums, 0.999... = 1 isn't. You can call
them all equations, sure, but the difference is that between "if I make
changes to X then it can equal Y" and "X already equals Y, even though they
appear to be different numbers".

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parfe
Very well then a sum based explanation:

    
    
      1/9 = .111...
      2/9 = .222...
      3/9 = .333...
      4/9 = .444...
      5/9 = .555...
      6/9 = .666...
      7/9 = .777...
      8/9 = .888...
      9/9 = .999... = 1
    

the .999 = 1 issue is not a math problem so much as a symbol issue. Those
fractional representations of ninths are presented to 4th graders if i recall
correctly, yet adults will argue that there must exist some number between
.999... and 1 even though both symbols represent the same value.

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corecirculator
I never had an issue with 0.999....=1, but after seeing so many articles on
internet I wonder if I'm missing something.

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basicxman
Yes but I could write this as

1 * 10^(-inf)

