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Full Idea
The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations.
Gist of Idea
Grouping by property is common in mathematics, usually using equivalence
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.63
| 9854 | We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett] |
| 9883 | Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |