Any real number in [0,1] has a unique binary decimal representation o.b1b2b3..., where each bi is either 0 or1. Numerically, o.b1b2b3...=from1 to ∞ Σ(bn/2n)
where the infinite series converge to a number in[0,1].
The question is- how does it possible for this series "to converge to a number in[0,1]" for example, how 1/3 can be expressed using this series? Is there a proof for that statement?
Thanks in advance