THERE IS NO OTHER NUMBER THAT THE SEQUENCE GETS ARBITRARILY CLOSE TO.
Thus, if you are going to assign a value to .9999… (going on
forever), the only sensible value is 1.
There is nothing special about .999… The idea that 1/3 = .3333…
is the same. None of .3, .33, .333333, etc. is exactly equal to 1/3,
but with each 3 added, the fraction is closer than the previous
approximation. In addition, 1/3 is the ONLY number that the series
gets arbitrarily close to.