Next | Continued Fraction Arithmetic | 43 |

Every real number

*r*has a unique representation as a continued fractionActually, like decimal expansions, it's

*not quite*uniqueEvery 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

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