A product set in arithmetic is the set of pairwise products of elements
of two sets ,
In particular, sumset sum-product problem
concerns simultaneous bounds on their cardinalities
(Zhang et al. 2026).
The term product set is also used for the Cartesian product , whose elements are ordered
pairs rather than products in the ambient ring
or field .
See also Cartesian Product ,
Sum-Product
Problem ,
Sumset
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References Zhang, K.; Zeng, Y.; and Wang, Y. "Ideal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product Exponent." 5 Oct 2026.
https://arxiv.org/abs/2610.05725 . Referenced
on Wolfram|Alpha Product Set
Cite this as:
Weisstein, Eric W. "Product Set." From
MathWorld https://mathworld.wolfram.com/ProductSet.html
Subject classifications
is the multiplicative analog of the sumset 
. The sum-product problem
concerns simultaneous bounds on their cardinalities
(Zhang et al. 2026).
