A math ???

LAST EDITED ON Jun-10-06 AT 10:12 AM (CST)
 
.999.... = 1
If x =.999...., then 10x = 9.999....
subtract x from 10x, 9.9999999.... - .9999999.... = 9
thus, 9x = 9 and x = 1, all legal moves.

>.999 = 1
>If x=.999, then 10x = 9.999
>subtract x from 10x, 9.999 - .999 = 9
>thus, 9x = 9 and x = 1, all legal moves.

I hate to say this but

if x=.999, then 10x = 9.990 (See the zero at the end? When multiplying by 10, add a zero.) Now:

subtract x from 10x, 9.990 - .999 = 8.991
thus 9x = 8.991 and x = .999

One must do correct math for it to be "legal moves."

Len, your math is excellant, my typing is not, I left an important piece of the puzzle out. I have edited it to make it the way it should read.

Following your latest logic, you are trying to go to infiinity without showing all of the numbers. Here is your latest:

.999.... = 1
If x =.999...., then 10x = 9.999....
subtract x from 10x, 9.9999999.... - .9999999.... = 9
thus, 9x = 9 and x = 1, all legal moves.

But you don't show all of the numbers, so you cannot properly do the math. There is still a zero at the end of the 10x equation.

It is like saying pi is 3.14 or 3.1416 or carry it out to whatever you want to. When you leave numbers off, you will not get a true calculation. The only way to get true accuracy is to carry it to the end or state that you have rounded it off. If you have rounded it off, it is not a legal proof.

If your lap times are 1.3 seconds and I round it off to 1 I will be looking for you to do six laps in six seconds. Then when I time you and it takes you 7.8 seconds I will think something is wrong. There is something wrong. I should not have rounded off the number.

Len's math is right. However, it is a matter of significant figures. If you start out with .999, you have three significant figures and that is the end of that!

LAST EDITED ON Jun-10-06 AT 07:58 PM (CST)
 
The series extends to infinity. There are only 9's in it.