Every real number r has a unique representation as a continued fraction
Actually, like decimal expansions, it's not quite unique
Every irrational number has a unique representation
Every rational number has exactly two representations
23/8 = 2 + 1/(1 + 1/7) = [2; 1, 7]
23/8 = 2 + 1/(1 + 1/(6 + 1/1)) = [2; 1, 6, 1]
As with decimal expansions, we sweep this under the carpet most of the time
With decimals, we choose the ..000.. form as canonical
With continued fractions, we choose the short form as canonical