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Minkowski question-mark function: Difference between revisions
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used an over/under style for the two possible continued fraction representations.
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m (used an over/under style for the two possible continued fraction representations.) |
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The question-mark function is continuous and monotonically increasing, so it has an inverse.
* Produce a function for {{math|?(x)}}. Be careful: rational numbers have two possible continued fraction representations
:::* {{math|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>]}} and
:::* {{math|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>−1,1]}}
* Choose one of the above that will give a binary expansion ending with a '''1'''.
* Produce the inverse function {{math|?<sup>-1</sup>(x)}}
* Verify that {{math|?(φ)}} = 5/3, where {{math|φ}} is the Greek golden ratio.
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