JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 2, Pages 277 - 287
(August 2003)
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ON
SOME CRITERIA FOR THE DENSITY OF THE RATIO SETS
OF POSITIVE INTEGERS
Jozsef Bukor (Slovakia) and Janos T. Toth (Czech Republic)
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Abstract: Let A,
B be subsets of positive integers. It
is shown that the density of the ratio sets
does not imply the density of the ratio
set
in the set of positive real numbers and
the reverse implication also need not be valid
in general. Further, it is proved that 1 is
the lower bound of a
’s for which
implies that
is everywhere dense in the set of all
positive real numbers. |
Keywords and phrases: asymptotic density, ratio set. |
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