Let
and
be finite subsets of positive real numbers. Solymosi gave the sum-product estimate
,
where
is the ceiling function. We use a variant of his argument to give the bound
(This isn’t quite a generalization since the logarithmic losses are worse here than in
Solymosi’s bound.)
Suppose that
is a finite subset of real numbers. We show that there exists an
such that
for some absolute
constant
.
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