Thomas A. Alspaugh
Properties of Operations
Under Construction
| Property | Definition for operations ● and ○ | As said in words |
|---|---|---|
| idempotent | X●X = X |
● is idempotent |
| commutative | X●Y = Y●X |
● is commutative |
| associative | (X●Y)●Z = X●(Y●Z) |
● is associative |
| distributive | X●(Y○Z) = (X●Y)○(X●Z) |
● distributes over ○ |
| absorptive | X●(X○Y) = X = X○(X●Y) |
● and ○ are mutually absorbtive |
Compare these with the reflexive, symmetric, and transitive properties of relations.
- thomas · alspaugh @ acm · org
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Attribution