# 2.9 recurring = 3 ! !!

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deep-techno
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16 Apr 2006, 2:41 pm

Here's some proof that 2.9 recurring is 3 (When a decimal digit reccurs then I will put a ¬ after it, eg. 2.9¬):

If 2.9¬ = x
Then 10x = 29.9¬ = 9x + x
9x = 10x - x = 29.9¬ - 2.9¬ = 27
x = 27/9 = 3

AbominableSnoCone
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16 Apr 2006, 3:41 pm

k3wlz0r

deep-techno
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16 Apr 2006, 4:18 pm

AbominableSnoCone wrote:
k3wlz0r

Well I understand the k3wl part but 'z0r'ry I don't understand the rest!

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Emettman
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16 Apr 2006, 5:27 pm

Did you discover this while staying at Hilbert's Hotel?

medianmistermustard
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16 Apr 2006, 5:31 pm

Works on any repeating decimal sequence really;

let x = .3repeating
10x = 3.3repeating = 9x + x
9x = 10x - x
9x = 3.3repeating - .3 repeating
9x = 3
x = 3/9 = 1/3

A lot easier that using geometric sums, which is how I first learned to prove stuff like that.

Neat.

alex
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16 Apr 2006, 5:49 pm

i figured this out in 6th grade although someone told me that the fraction thing was just a rough conversion and what you're stipulating to be true is actually not true and just something people say is true to make conversions easy.

Now I'm just confused. As a result, I haven't gotten a good grade in math since then.

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reneviht
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16 Apr 2006, 7:05 pm

It could be they didn't notice the repeating decimal was supposed to be repeating. 0.9 repeating is most certainly a geometric series, and as long as you're working in decimal, it's equal to 1. Unless, of course, there's some funky metric that you're using... I've heard of metrics where the sequence 7, 49, 343, 2401, ..., 7^n, ... converges to a real number. But for the life of me, I can't remember where I heard it in reference to.

jonathan79
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16 Apr 2006, 11:44 pm

Emettman wrote:
Did you discover this while staying at Hilbert's Hotel?

I think it was a Holiday Inn-

jammie
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17 Apr 2006, 3:50 am

hiya,

We did this in maths a while ago. the thing is it proves that 2.9¬ x 9 = a whole number.

2.9¬ will always be 2.9¬ at no point is it 3.

jammie

deep-techno
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17 Apr 2006, 6:19 am

It was in a science magazine I bought last August and it says that 2.9¬ = 3. Well, everybody makes mistakes.

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Emettman
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17 Apr 2006, 2:05 pm

jonathan79 wrote:
Emettman wrote:
Did you discover this while staying at Hilbert's Hotel?

I think it was a Holiday Inn-

Do they have infionite rooms too? And are they all full?

Bland
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17 Apr 2006, 9:27 pm

What can I say? I've only recently figured out the subtle differences between natural and whole numbers and integers. (sad, huh? Either a testament to my stupidity or public education)

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TheBladeRoden
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17 Apr 2006, 9:37 pm

jonathan79 wrote:
Emettman wrote:
Did you discover this while staying at Hilbert's Hotel?

I think it was a Holiday Inn-

Holiday Inn Express

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reneviht
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21 Apr 2006, 1:59 pm

jammie wrote:
2.9¬ will always be 2.9¬ at no point is it 3.

Which of the maths did you do this in?

I assumed that we were talking about real numbers with the metric defined as d(x, y) = |x - y|, and that 2.9¬ was referring to the limit of the sequence

a_0 = 2
a_n = 9/10^n + a_(n-1)

(normally, I'd define it as a series using summation notation, but I don't think HTML can do that). The axiom of completeness applies to the reals, so the limit of a_n = a is a real number. Since for all e > 0, |a - 3| < e, doesn't this mean the limit is equal to 3 (unless I made a typo in the definition of the sequence)?

DrizzleMan
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22 Apr 2006, 7:56 am

Yeah, as far as I know it's just two ways of writing 3. Just like 23426345.3269¬ is another way of writing 23426345.327

Anyone who says 0.9¬ isn't the same as 1 is confusing notation with storage. Computers storing 0.3¬ might round it to 0.3333333 (a finite number of 3's) so when you multiply you get 0,9999999 which doesn't equal 1. (Of course, computers round in binary, not decimal, this is just an analogy)

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kraftiekortie
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03 Jan 2019, 5:33 pm

2.9999 (to infinity) is never 3!! !! !! !