Originally Posted by
omnitarian
Couldn't you consider .999... sticking a 9 after a series of infinite nines?
It'd be part of the infinite string of 9's, so you could simplify it back to 0.999... and not have the contradiction
SeedRankLou: Simplifying the final solution makes sense (and makes things more readable too), although I wouldn't say working in simplest terms all the time is necessary during the working out stage of your solution. For example, I might prefer not to simplify certain algebraic expressions in an equation because I might foresee the need to unsimplify it again later on to get some terms to cancel out more easily. Or when working out nth roots of complex numbers in (r,theta) notation, you want to take into account values which are not the simplest or principal value of your number if you want to get all solutions.
