Equivalence Class

An equivalence class is defined as a Subset of the form , where is an element of and theNotation ``'' is used to mean that there is an Equivalence Relation between and . It can be shownthat any two equivalence classes are either equal or disjoint, hence the collection of equivalence classes forms a partition of. For all , we have Iff and belong to the same equivalence class.

A set of Class Representatives is a Subset of which contains Exactly Oneelement from each equivalence class.

For a Positive Integer, and Integers, consider the Congruence ,then the equivalence classes are the sets , etc. The standard Class Representatives are taken to be 0, 1, 2, ...,.

References

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 56-57, 1993.

• Spider Lines
• Spiegeldrieck
• Spieker Center
• Spieker Circle
• Spigot Algorithm
• Spijker's Lemma
• Spindle Cyclide
• Spindle Torus
• Spinode
• Spinor
• Spiral
• Spiral Point
• Spira Mirabilis
• Spiric Section
• Spirograph
• Spirolateral
• Spline
• Splitting
• Splitting Algorithm
• Sponge
• Sporadic Group
• Sports
• Sprague-Grundy Function
• Sprague-Grundy Number
• Sprague-Grundy Value