0.999....=1

[Teeqoz]

JRPGfan said:

Teeqoz said:

You are thinking of it as more like a very long but finite list of 9s.

0.000...1 wouldn't work.  You can't have an infinite number of zeroes followed by a 1, because the zeroes go on forever, there is no end, so there will never be a zero after which you can place the 1. It's like saying "There's a 1 in the infiniteth decimal place". That decimal place doesn't exist, because if it did, it would have been finite.

The same is true for 0.999999999 though.

Why do you have it work for one thing but not another?

The proof looks solid enough though, the concept itself is what I have a hard time wrapping my mind around.

 

Note Im not saying that 0 is the same as 0.0000000 ect 1.

Im saying that 0.99999999 will always be missing that 0.00000000 ect 1 part, that keeps it from being a pure 1.

No, saying that there is an infinite sequence of 9s doesn't require and end. It goes on forever. However to say that there is an infinite sequence of 0s, followed by a 1 doesn't work. There can't be a 1 after the infinite amount of 0s, because that would by definition mean it was a finite amount of 0s.

That said, I can understand why you have a hard time figuring it out. It can be hard to wrap your head around it.