1=0.9999...

What the hell?! ???

http://a3.sphotos.ak.fbcdn.net/hphotos-ak-snc7/s320x320/426968_10150564248008360_290539813359_8773764_606312421_n.jpg

Well, well … apparently it does!

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

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

Thanks, Mefiante. 8)

I saw this first with dawkin’s scale discussions :wink:

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?

From your last step above:

10a = 9 + a
=> 10a - a = 9 + a - a (subtract a from both sides)
=> 9a = 9

Thank you, briandvds, I follow that :slight_smile: