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WDAddition modulo n

Definition·D115

Add residue classes by adding representatives and taking the class of the result.

For and residue classes in (D114), addition is given on representatives by for , with on the right the addition of integers.
In words
The sum of two residue classes is the class of the sum of any chosen representatives.
Never needed: F03 · F04 · F05 · F06 · F08 · F10 · F11 · F12 · F13 · A03 · A04 · A05 · A07 · A08 · A09 (computed from the citation graph, not asserted).

Remarks

Well defined: by L74, if and then , so the result does not depend on the representatives chosen. Under this operation is an abelian group with identity and the negative of equal to (part of T59). This is clock arithmetic: modulo , .

Used by