That is a good approach but it seems more algebraic proof then geometric. Are you naturally good at mathematical induction? (If that is what its called..)

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- Jan 5th 2007, 01:09 PManthmoo
- Jan 5th 2007, 01:15 PManthmoo
Ah I understand now - blame the imagination, I had an image of a perfect machine (that copes with infinity) drawing a perfect circle and it could never complete the circle..

I've had this problem before, such as with

0.9999999...=1 then i realised 1/9 * 9 = 1

which similarly relates to the point that you made! - Jan 5th 2007, 01:22 PMtopsquark
Well, presumably we can never walk anywhere because you start by walking half the distance, then you walk half THAT distance, then half of that distance, etc, so you can never get to your destination. Blame Zeno (or whoever came up with that concept.) Of course, he never took Physics. :D

-Dan - Jan 5th 2007, 04:38 PMQuick
just an interesting way to look at it (I know I saw this on the forum here, I just don't know where)

Let's say that $\displaystyle n=0.9\bar{9}$

Then: $\displaystyle 10n=9.9\bar{9}$

Therefore: $\displaystyle 10n-n=9.9\bar{9}-0.9\bar{9}$

So then: $\displaystyle 9n=9\quad\Longrightarrow\quad \boxed{n=1}$ - Jan 6th 2007, 02:09 PMThePerfectHacker
- Jan 6th 2007, 04:05 PMTriKri