yes, according to abstract mathematical laws, it can be proved that 0.9999 (with infinite such 9's) will definitely be equal to 1 (as proved by raj87verma88)...
However, since the value of infinity can't be realized in real life, such an application is not possible for generating solutions to mathematical problems dealing with practical physics and other sciences
I might sound confusing, but then "God doesn't exactly play dice"
, and there just might be some really great reason why we can't prove that 0.99999999 (till infinity) is not equal to 1 ...