Journal title
Integers
Volume
20A
Last updated
2021-10-19T13:24:04.47+01:00
Page
1-9
Abstract
© 2020, Colgate University. All rights reserved. For a real number x and set of natural numbers A, define x * A:= {xa mod 1: A ϵ A} ⊆ (0, 1). We consider relationships between x, A, and the order-type of x * A. For example, for every irrational x and countable order-type ↵, there is an A with x * A⁓α, but if ↵ is a well order, then A must be a thin set. If, however, A is restricted to be a subset of the powers of 2, then not every order type is possible, although arbitrarily large countable well orders arise.
Symplectic ID
1147269
Submitted to ORA
Off
Publication type
Journal Article
Publication date
1 January 2020