1=0.9999...

(1/2) > >>

 Rigil Kent (January 31, 2012, 08:44:19 AM):
What the hell?! ???

 Rigil Kent (January 31, 2012, 09:18:28 AM):
Well, well ... apparently it does!
 Mefiante (January 31, 2012, 09:31:44 AM):
Yes, it’s true. The proof shown in the OP is the standard one. Another proof can be framed in terms of the sum of a convergent geometric series with the ratio of consecutive terms equal to 1/10 = 0.1 (exact). (As an aside, this counterintuitive fact illustrates that infinity in mathematics is not as simple a concept as one might think.)

A mathematically less rigorous way to think about it is as follows:

1/3 = 0.333333…

Then 1/3 + 1/3 + 1/3 = 0.333333… + 0.333333… + 0.333333… = 0.999999…

But 1/3 + 1/3 + 1/3 = 3/3 = 1.

Therefore 0.999999… = 1. QED.

'Luthon64
 Rigil Kent (January 31, 2012, 09:49:12 AM):
A mathematically less rigorous way to think about it is as follows:

1/3 = 0.333333…

Then 1/3 + 1/3 + 1/3 = 0.333333… + 0.333333… + 0.333333… = 0.999999…

But 1/3 + 1/3 + 1/3 = 3/3 = 1.

Therefore 0.999999… = 1. QED.

'Luthon64

Very convincing for sure. It's somehow more intuitive than the proof in the OP.

Thanks, Mefiante. 8)
 cyghost (January 31, 2012, 10:14:40 AM):
I saw this first with dawkin's scale discussions ;)

So I follow the first proof untill here:

a = 0.999...
10a = 9.999...
10a = 9 + 0.999...
10a = 9 + a

why is 9a now 9 please?