What I know is:
1/3 does not equal 0.3333~ Logically, if we made that infinitely long it would never equal 1/3, just like with the limit of a function:
lim x->a f(x) = L, means that f(x) will be arbitarily close to L provided x is sufficiently close to a, but not equal to a.
1/3 != 0.3333~
3 x 1/3 = 1
3 x 0.3333~ = 0.9999~