>>152
If you read the fucking proof, it doesn't matter that it's an infinitely long decimal. The first operation performed is multiplying 0.999~ by 10. This clearly produces 9.999~ Then, you subtract off the quantity 0.999~. That's it.
>>155
It's debated? That's fucking news to me. Oh wait, you mean it's debated by little 14 year old shits on the internet who know nothing about mathematics. Oh, and there are plenty of definite(gb2/spelling/) laws about infinities. Learn Calculus.