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Abstract In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of… Click to show full abstract
Abstract In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of that set. We consider more general missing digit sets $C$ and construct numbers in $C$ that are arbitrarily well approximable by rationals in $C$ , but badly approximable by rationals outside of $C$ . More precisely, we construct them so that all but finitely many of their convergents lie in $C$ .
Keywords:
convergents cantor;
numbers almost;
cantor set;
almost convergents
Journal Title: Canadian Mathematical Bulletin
Year Published: 2019
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Journal Title: Canadian Mathematical Bulletin
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!