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Full Idea
For two overlapping individuals their 'product' is the individual which is part of both and such that any common part of both is part of it, expressed by 'x · y', read as 'the product of x and y'.
Clarification
Aka 'binary product'
Gist of Idea
Product: the product of two individuals is the sum of all of their overlaps, written 'x · y'
Source
Peter Simons (Parts [1987], 1.1.05)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.13
A Reaction
That is, the 'product' is the sum of any common parts between two individuals. In set theory all sets intersect at the null set, but mereology usually avoids the 'null individual'.