<p>1/3 = 0.33333…
(1/3)<em>3 = 0.33333…</em>3
1 = 0.99999…</p>
<p>HOWEVER, 1/3 = 0.33333… this expression on the right seems to me that it APPROACHES to 1/3 but its not exactly 1/3 theoretically. Seems to me that:
0.33333… = limit (as A approaches to infinity) sigma(from n=1 to n=A) (3/10^n)
so
0.99999… = limit (as A approaches to infinity) sigma(from n=1 to n=A) (9/10^n)
as all theoretical mathematicians should know the limit from the right side is not necessarily equal to the left side, but it APPROACHES to it.</p>
<p>Practically, 1 = 0.99999…
Theoretically, it’s not supposed to if we consider the definition of the limit</p>