Because what is more fun than discussing math, right?

Also 0.999... is here used to denote a zero, followed by infinite 9s. Also reffered to as 0.9 reccurring, and many other things.

If                  x=0.999...

10x=9.999...

10x=9+0.999...

10x=9+x

 10x-x=9

 9x=9

 9x/9=9/9

  x=1

Alternatively:

1/9=0.111...

0.111...*9=0.999...

0.111...*9=1/9*9=9/9=1

What to people think about this?

I have no words. This thing always gets me. Even with the idea of rounding it doesn't validate any other number's identity. Why just these two?! O.o

How do you go from:

10x = 9+x

to

10x-x=9   <---- (isnt this part wrong?)

Shouldnt it be:

(10x)/x = 9     =>

9x = 9

your doing division by X, on both sides of the equation right? to move the x on the side of the 9, across.

*edit: Just noticed you have the 9x = 9 part, so doesnt matter lol.

Actually, all numbers have two notations.

1.5000... (or 1.5 as we'd normally write) is the same as 1.4999....

0.1000... is the same as 0.09999999 (this one is pretty easy to infer when one accepts that 0.999... is equal to 1, because 0.0999 is the same as 0.999.../10, and 0.1 is the same as 1/10, and because 0.999...=1, naturally 0.1 must be equal to 0.0999...)

No, I'm not dividing by x, I'm subtracting x on both sides.

I could've written

10x=9+x

10x-x=9+x-x

But that's just writing things unnecessarily messy.

I didn't believe it at first but it is real. Infinity is a concept, not a number.

no he's subtracting x.

If he was dividing by x it would be as follows:

10x = 9+x

10*(x/x) = 9 + (x/x)

Obviously (x/x) is 1, so

10*1 = 9 + 1

10 = 10

considering you want a result that is "x = ..." it wouldn't make sense to divide by x in that case.

Versus_Evil said:

9 (smirk)

Are you allowed to do that? isnt that bad math?

I cant even remember, I just thought you where supposed to divide by x on both sides to get the x out.

But it doesnt matter, you still reach the same 9x = 9.

Such a weird, but cool result. One of the most counterintuitive concepts I've ever heard.