structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes

[classes created by close relationships of members]

7 ideas
We can introduce new objects, as equivalence classes of objects already known [Dummett on Frege]
Frege introduced the standard device, of defining logical objects with equivalence classes [Dummett on Frege]
We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton]
An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton]
Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
Grouping by property is common in mathematics, usually using equivalence [George/Velleman]
'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman]