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Single Idea 9716

[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes ]

Full Idea

Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set.

Gist of Idea

We 'partition' a set into distinct subsets, according to each relation on its objects

Source

Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0)

Book Ref

Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.6

The 7 ideas with the same theme [classes created by close relationships of members]:

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]