Some properties of the set of Liouville numbers
DOI:
https://doi.org/10.5902/2179460X65058Keywords:
Liouville Numbers, Transcendence, Hausdorff Measure, Irrationality Measure, Irrational NumbersAbstract
The present work consists on the introduction of the Transcendental Number Theory beginnings. First, we will present the classical theorems of the rational approximations, finishing with the theorem of Hurwtiz-Markov. The following part is about Liouville Numbers and their intrinsic properties, proving their transcendence. Also, we will talk about the measure of irrationality, an interesting way to classify the degree of irrationality of certain real number. The last (but not least) topic is about the Liouville numbers as a set and their paradoxes, this set, in the view of the topology, is the complement of a Meagre set, which this means that is "big". However, on the analysis point of view, the Liouville Numbers has null measure, considering the Lebesgue and Hausdorff measures.
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- 2022-07-07 (3)
- 2022-06-15 (2)
- 2022-04-18 (1)
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