Minkowski question-mark function: Difference between revisions

show what the two different representations of a continued fraction are
m (correct a typo in the task description)
(show what the two different representations of a continued fraction are)
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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 the one 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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