the zarzuela

(x + cx + ____) = (x + ____)^2
(suggested new terminology, to give a handle to a crucial maneuver in algebra)
keywords: Mathematics, manipulation, quadratic formula

QUERY

Let’s call a collection of sets a fleet. Partitions are fleets encountered early on in one’s study of mathematics. Let us call a fleet-in-being a fleet that is not a partition. Then: what is the first naturally-occurring (i.e., well-motivated) fleet-in-being that one encounters in one’s study of mathematics? Is it the collection of all convex sets containing a given set?
keywords: Set Theory, pedagogy