⌊α⌋,⌊2α⌋,⌊3α⌋,… and ⌊β⌋,⌊2β⌋,⌊3β⌋,…
Let α and β be positive irrational numbers such that the sequences above contain every positive integer exactly once. i.e. If you pick a positive integer, it will appear in only one of the above sequences. Which of the following statements are true?
Notation: ⌊⋅⌋ denotes the floor function.