OpenEuphoria

Re: Puzzle

• Posted by Patrick Barnes <mrtrick at gmail.com> Aug 11, 2004
• 393 views

On Wed, 11 Aug 2004 04:32:17 -0700, Matt Lewis <guest at rapideuphoria.com>
wrote:
> What he meant was infinitely repeating 9's.  And this is a true statement.
> It's a funny thing about limits and infinities.  Here's a proof:
> 
> Let x = 0.9_ (I'll use _ to indicate an infinite sequence of 9's).  

That's the first problem. 0.9_ is in fact 1. 0.9_ is not a number, but
a representation of a geometric series... which when evaluated with a
limit of INF, returns 1.

<edited>
> If you multiply both sides by 10, you get:
> 
> 10x = 10
> 
> Since we know that x = 1, if we subtract x from both sides, we get:
> 
> 9x = 9 or x = 1.  Therefore 1 = 1. Hmmm, quite unexpected.
> 
What about this one? 

x = 1,  y = 1

x = y
x^2 = xy     (times both sides by x)
x^2 - y^2 = xy - y^2  (subtract y^2 from both sides)
(x+y)(x-y) = y(x-y)   (factorise)
x+y = y (divide both sides by (x-y)

y = x+y
1 = 1+ 1
1 = 2???
(I know there is a fallacy here, I'm not seriously supporting this)

-- 
MrTrick