impossible statements

[Dan Zollman]

I actually just realized I should have done a search on this topic before posting so that I don't post the same topic again, and I found this:
http://www.chiefdelphi.com/forums/sh...ad.php?t=24368

A variation of the first proof was in that thread, and even though the thread is a year and a half old, I shouldn't have mentioned it.

But I still want to know what people have to say about thes kind of mathematical proof. I think it's a very interesting subject.

[sanddrag]

I don't know about that one (I actually don't have time to read it at the moment) but what about this.

1/9 = .11111 continuing
2/9 = .222222 continuing
etc etc
8/9 = .88888 continuing

9/9 = ? .9999 continuing or 1 exactly? I know .9999 continuing is realy close to 1 but still it makes you wonder.

[Alan Anderson]

Originally Posted by sanddrag

9/9 = ? .9999 continuing or 1 exactly? I know .9999 continuing is realy close to 1 but still it makes you wonder.

".9999 continuing" is equal to 1.

[sanddrag]

Originally Posted by Alan Anderson

".9999 continuing" is equal to 1.

How do you figure? You are always going to have that really small (but existant) 0.00000...00001 left over. I see 0.999 continuing as approaching 1 but I am inclined to think it never actually gets there.

[Alan Anderson]

Originally Posted by Alan Anderson

".9999 continuing" is equal to 1.

Originally Posted by sanddrag

How do you figure? You are always going to have that really small (but existant) 0.00000...00001 left over. I see 0.999 continuing as approaching 1 but I am inclined to think it never actually gets there.

Your position is based on the false impression that the 9s eventually run out, leaving a bit left unaccounted for. They don't; that's what repeating decimals are all about.

Figuring it is easy:

       x = 0.9999...
     10x = 9.9999...
 10x - x = 9.9999... - 0.9999...
      9x = 9
       x = 1

See also http://en.wikipedia.org/wiki/Recurri..._of_0.99999... for other ways to demonstrate it.

[jdiwnab]

Originally Posted by Alan Anderson

Your position is based on the false impression that the 9s eventually run out, leaving a bit left unaccounted for. They don't; that's what repeating decimals are all about.

It is also similer to Limit of x as x approches 1. This isn't what is x when x is one, but you could treat it like that because x can be 1. you are so close to one that it might as well be one