Doting, Joris (2022) Minkowski’s Question Mark Function. Bachelor's Thesis, Mathematics.
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Abstract
Minkowski’s question mark function ?(x) establishes a relation between quadratic irrationals, non-dyadic rationals and dyadic rational numbers. This paper will work out the preliminary notions of modified Farey sequences, dyadic rational sequences and continued fraction expansions. We will prove certain properties of these notions, and use those to establish an equivalent but more workable definition of Minkwoski’s question mark function. We will use both definitions to approximate some as of yet unknown fixed points of ?(x). We will conclude with a proof that this function is singular. This amounts to showing that it is continuous and non-constant, yet has derivative 0 almost everywhere.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Sterk, A.E. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 30 May 2022 08:45 |
| Last Modified: | 30 May 2022 08:45 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27101 |
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