That's what I had always thought, until I saw a few proofs that seemed to say otherwise! Here's one:
x = 0.999... 10x = 9.999... (Multiply by ten) 9x = 9 (Subtracts 0.999...) x = 1 = 0.999... (Divides by 9!)
So this is where I see a weird problem! Today, though, I was thinking and though that when you multiply by ten, aren't there infinity - 1 nines after the decimal? That would make 9x = 8.9999...1 and x = (...Works it out on calculator) 0.999.... Oh so... wait what XD ! I guess I kind of just figured that out on my own!
But am I right in saying there are infinity - 1 nines after the decimal?
And now I'm confused about another thing. How can 0.999..., a rational number, be represented as a fraction?! 9/9 is 1 but anything over 9 is supposed to be that number repeating, (after the decimal place).